The best problems from around the world - Các đề thi toán toàn thế giới

PREFACE

Collecting the Mathematics tests from the contests choosing the best students is not

only my favorite interest but also many different people’s. This selected book is an adequate

collection of the Math tests in the Mathematical Olympiads tests from 14 countries, from

different regions and from the International Mathematical Olympiads tests as well.

I had a lot of effort to finish this book. Besides, I’m also grateful to all students

who gave me much support in my collection. They include students in class 11 of specialized

Chemistry – Biologry, class 10 specialized Mathematics and class 10A2 in the school year

2003 – 2004, Nguyen Binh Khiem specialized High School in Vinh Long town.

This book may be lack of some Mathematical Olympiads tests from different

countries. Therefore, I would like to receive both your supplement and your supplementary

ideas. Please write or mail to me.

• Address: Cao Minh Quang, Mathematic teacher, Nguyen Binh Khiem specialized

High School, Vinh Long town.

• Email: [email protected]

Vinh Long, April 2006

Cao Minh Quang

☺ The best problems from around the world Cao Minh Quang

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Abbreviations

AIME American Invitational Mathematics Examination

ASU All Soviet Union Math Competitions

BMO British Mathematical Olympiads

CanMO Canadian Mathematical Olympiads

INMO Indian National Mathematical Olympiads

USAMO United States Mathematical Olympiads

APMO Asian Pacific Mathematical Olympiads

IMO International Mathematical Olympiads

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CONTENTS

Page

Preface................................................................................................................................. 1

Abbreviations ...................................................................................................................... 2

Contents............................................................................................................................... 3

PART I. National Olympiads.......................................................................................... 17

1. AIME (1983 – 2004) ..................................................................................................... 17

1.1. AIME 1983............................................................................................................ 18

1.2. AIME 1984............................................................................................................ 20

1.3. AIME 1985............................................................................................................ 21

1.4. AIME 1986............................................................................................................ 23

1.5. AIME 1987............................................................................................................ 24

1.6. AIME 1988............................................................................................................ 25

1.7. AIME 1989............................................................................................................ 26

1.8. AIME 1990............................................................................................................ 27

1.9. AIME 1991............................................................................................................ 28

1.10. AIME 1992.......................................................................................................... 29

1.11. AIME 1993.......................................................................................................... 30

1.12. AIME 1994.......................................................................................................... 32

1.13. AIME 1995.......................................................................................................... 33

1.14. AIME 1996.......................................................................................................... 35

1.15. AIME 1997.......................................................................................................... 36

1.16. AIME 1998.......................................................................................................... 37

1.17. AIME 1999.......................................................................................................... 39

1.18. AIME 2000.......................................................................................................... 40

1.19. AIME 2001.......................................................................................................... 42

1.20. AIME 2002.......................................................................................................... 45

1.21. AIME 2003.......................................................................................................... 48

1.22. AIME 2004.......................................................................................................... 50

2. ASU (1961 – 2002)......................................................................................................... 51

2.1. ASU 1961.............................................................................................................. 52

2.2. ASU 1962.............................................................................................................. 54

2.3. ASU 1963.............................................................................................................. 55

2.4. ASU 1964.............................................................................................................. 56

2.5. ASU 1965.............................................................................................................. 57

2.6. ASU 1966.............................................................................................................. 59

2.7. ASU 1967.............................................................................................................. 60

2.8. ASU 1968.............................................................................................................. 61

2.9. ASU 1969.............................................................................................................. 63

2.10. ASU 1970............................................................................................................ 64

2.11. ASU 1971............................................................................................................ 65

2.12. ASU 1972............................................................................................................ 67

2.13. ASU 1973............................................................................................................ 68

2.14. ASU 1974............................................................................................................ 70

2.15. ASU 1975............................................................................................................ 72

2.16. ASU 1976............................................................................................................ 74

2.17. ASU 1977............................................................................................................ 76

2.18. ASU 1978............................................................................................................ 78

2.19. ASU 1979............................................................................................................ 80

2.20. ASU 1980............................................................................................................ 82

2.21. ASU 1981............................................................................................................ 84

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2.22. ASU 1982............................................................................................................ 86

2.23. ASU 1983............................................................................................................ 88

2.24. ASU 1984............................................................................................................ 90

2.25. ASU 1985............................................................................................................ 92

2.26. ASU 1986............................................................................................................ 94

2.27. ASU 1987............................................................................................................ 96

2.28. ASU 1988............................................................................................................ 98

2.29. ASU 1989........................................................................................................... 100

2.30. ASU 1990........................................................................................................... 102

2.31. ASU 1991........................................................................................................... 104

2.32. CIS 1992............................................................................................................. 106

2.33. Russian 1995 ..................................................................................................... 108

2.34. Russian 1996 ...................................................................................................... 110

2.35. Russian 1997 ...................................................................................................... 112

2.36. Russian 1998 ...................................................................................................... 114

2.37. Russian 1999 ...................................................................................................... 116

2.38. Russian 2000 ...................................................................................................... 118

2.39. Russian 2001 ...................................................................................................... 121

2.40. Russian 2002 ...................................................................................................... 123

3. BMO (1965 – 2004) ..................................................................................................... 125

3.1. BMO 1965............................................................................................................ 126

3.2. BMO 1966............................................................................................................ 127

3.3. BMO 1967............................................................................................................ 128

3.4. BMO 1968............................................................................................................ 129

3.5. BMO 1969............................................................................................................ 130

3.6. BMO 1970............................................................................................................ 131

3.7. BMO 1971............................................................................................................ 132

3.8. BMO 1972............................................................................................................ 133

3.9. BMO 1973............................................................................................................ 134

3.10. BMO 1974.......................................................................................................... 136

3.11. BMO 1975.......................................................................................................... 137

3.12. BMO 1976.......................................................................................................... 138

3.13. BMO 1977.......................................................................................................... 139

3.14. BMO 1978.......................................................................................................... 140

3.15. BMO 1979.......................................................................................................... 141

3.16. BMO 1980.......................................................................................................... 142

3.17. BMO 1981.......................................................................................................... 143

3.18. BMO 1982.......................................................................................................... 144

3.19. BMO 1983.......................................................................................................... 145

3.20. BMO 1984.......................................................................................................... 146

3.21. BMO 1985.......................................................................................................... 147

3.22. BMO 1986.......................................................................................................... 148

3.23. BMO 1987.......................................................................................................... 149

3.24. BMO 1988.......................................................................................................... 150

3.25. BMO 1989.......................................................................................................... 151

3.26. BMO 1990.......................................................................................................... 152

3.27. BMO 1991.......................................................................................................... 153

3.28. BMO 1992.......................................................................................................... 154

3.29. BMO 1993.......................................................................................................... 155

3.30. BMO 1994.......................................................................................................... 156

3.31. BMO 1995.......................................................................................................... 157

3.32. BMO 1996.......................................................................................................... 158

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3.33. BMO 1997.......................................................................................................... 159

3.34. BMO 1998.......................................................................................................... 160

3.35. BMO 1999.......................................................................................................... 161

3.36. BMO 2000.......................................................................................................... 162

3.37. BMO 2001.......................................................................................................... 163

3.38. BMO 2002.......................................................................................................... 164

3.39. BMO 2003.......................................................................................................... 165

3.40. BMO 2004.......................................................................................................... 166

4. Brasil (1979 – 2003) .................................................................................................... 167

4.1. Brasil 1979 ........................................................................................................... 168

4.2. Brasil 1980 ........................................................................................................... 169

4.3. Brasil 1981 ........................................................................................................... 170

4.4. Brasil 1982 ........................................................................................................... 171

4.5. Brasil 1983 ........................................................................................................... 172

4.6. Brasil 1984 ........................................................................................................... 173

4.7. Brasil 1985 ........................................................................................................... 174

4.8. Brasil 1986 ........................................................................................................... 175

4.9. Brasil 1987 ........................................................................................................... 176

4.10. Brasil 1988 ......................................................................................................... 177

4.11. Brasil 1989 ......................................................................................................... 178

4.12. Brasil 1990 ......................................................................................................... 179

4.13. Brasil 1991 ......................................................................................................... 180

4.14. Brasil 1992 ......................................................................................................... 181

4.15. Brasil 1993 ......................................................................................................... 182

4.16. Brasil 1994 ......................................................................................................... 183

4.17. Brasil 1995 ......................................................................................................... 184

4.18. Brasil 1996 ......................................................................................................... 185

4.19. Brasil 1997 ......................................................................................................... 186

4.20. Brasil 1998 ......................................................................................................... 187

4.21. Brasil 1999 ......................................................................................................... 188

4.22. Brasil 2000 ......................................................................................................... 189

4.23. Brasil 2001 ......................................................................................................... 190

4.24. Brasil 2002 ......................................................................................................... 191

4.25. Brasil 2003 ......................................................................................................... 192

5. CanMO (1969 – 2003) ................................................................................................. 193

5.1. CanMO 1969 ........................................................................................................ 194

5.2. CanMO 1970 ........................................................................................................ 195

5.3. CanMO 1971 ........................................................................................................ 196

5.4. CanMO 1972 ........................................................................................................ 197

5.5. CanMO 1973 ........................................................................................................ 198

5.6. CanMO 1974 ........................................................................................................ 199

5.7. CanMO 1975 ........................................................................................................ 200

5.8. CanMO 1976 ........................................................................................................ 201

5.9. CanMO 1977 ........................................................................................................ 202

5.10. CanMO 1978 ...................................................................................................... 203

5.11. CanMO 1979 ...................................................................................................... 204

5.12. CanMO 1980 ...................................................................................................... 205

5.13. CanMO 1981 ...................................................................................................... 206

5.14. CanMO 1982 ...................................................................................................... 207

5.15. CanMO 1983 ...................................................................................................... 208

5.16. CanMO 1984 ...................................................................................................... 209

5.17. CanMO 1985 ...................................................................................................... 210

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5.18. CanMO 1986 ...................................................................................................... 211

5.19. CanMO 1987 ...................................................................................................... 212

5.20. CanMO 1988 ...................................................................................................... 213

5.21. CanMO 1989 ...................................................................................................... 214

5.22. CanMO 1990 ...................................................................................................... 215

5.23. CanMO 1991 ...................................................................................................... 216

5.24. CanMO 1992 ...................................................................................................... 217

5.25. CanMO 1993 ...................................................................................................... 218

5.26. CanMO 1994 ...................................................................................................... 219

5.27. CanMO 1995 ...................................................................................................... 220

5.28. CanMO 1996 ...................................................................................................... 221

5.29. CanMO 1997 ...................................................................................................... 222

5.30. CanMO 1998 ...................................................................................................... 223

5.31. CanMO 1999 ...................................................................................................... 224

5.32. CanMO 2000 ...................................................................................................... 225

5.33. CanMO 2001 ...................................................................................................... 226

5.34. CanMO 2002 ...................................................................................................... 227

5.35. CanMO 2003 ...................................................................................................... 228

6. Eötvös Competition (1894 – 2004) .............................................................................. 229

6.1. Eötvös Competition 1894..................................................................................... 230

6.2. Eötvös Competition 1895..................................................................................... 230

6.3. Eötvös Competition 1896..................................................................................... 230

6.4. Eötvös Competition 1897..................................................................................... 230

6.5. Eötvös Competition 1898..................................................................................... 231

6.6. Eötvös Competition 1899..................................................................................... 231

6.7. Eötvös Competition 1900..................................................................................... 231

6.8. Eötvös Competition 1901..................................................................................... 231

6.9. Eötvös Competition 1902..................................................................................... 232

6.10. Eötvös Competition 1903................................................................................... 232

6.11. Eötvös Competition 1904................................................................................... 232

6.12. Eötvös Competition 1905................................................................................... 232

6.13. Eötvös Competition 1906................................................................................... 233

6.14. Eötvös Competition 1907................................................................................... 233

6.15. Eötvös Competition 1908................................................................................... 233

6.16. Eötvös Competition 1909................................................................................... 233

6.17. Eötvös Competition 1910................................................................................... 234

6.18. Eötvös Competition 1911................................................................................... 234

6.19. Eötvös Competition 1912................................................................................... 234

6.20. Eötvös Competition 1913................................................................................... 234

6.21. Eötvös Competition 1914................................................................................... 235

6.22. Eötvös Competition 1915................................................................................... 235

6.23. Eötvös Competition 1916................................................................................... 235

6.24. Eötvös Competition 1917................................................................................... 235

6.25. Eötvös Competition 1918................................................................................... 236

6.26. Eötvös Competition 1922................................................................................... 236

6.27. Eötvös Competition 1923................................................................................... 236

6.28. Eötvös Competition 1924................................................................................... 236

6.29. Eötvös Competition 1925................................................................................... 237

6.30. Eötvös Competition 1926................................................................................... 237

6.31. Eötvös Competition 1927................................................................................... 237

6.32. Eötvös Competition 1928................................................................................... 237

6.33. Eötvös Competition 1929................................................................................... 238

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6.34. Eötvös Competition 1930................................................................................... 238

6.35. Eötvös Competition 1931................................................................................... 238

6.36. Eötvös Competition 1932................................................................................... 238

6.37. Eötvös Competition 1933................................................................................... 239

6.38. Eötvös Competition 1934................................................................................... 239

6.39. Eötvös Competition 1935................................................................................... 239

6.40. Eötvös Competition 1936................................................................................... 240

6.41. Eötvös Competition 1937................................................................................... 240

6.42. Eötvös Competition 1938................................................................................... 240

6.43. Eötvös Competition 1939................................................................................... 240

6.44. Eötvös Competition 1940................................................................................... 241

6.45. Eötvös Competition 1941................................................................................... 241

6.46. Eötvös Competition 1942................................................................................... 241

6.47. Eötvös Competition 1943................................................................................... 242

6.48. Eötvös Competition 1947................................................................................... 242

6.49. Eötvös Competition 1948................................................................................... 242

6.50. Eötvös Competition 1949................................................................................... 242

6.51. Eötvös Competition 1950................................................................................... 243

6.52. Eötvös Competition 1951................................................................................... 243

6.53. Eötvös Competition 1952................................................................................... 243

6.54. Eötvös Competition 1953................................................................................... 244

6.55. Eötvös Competition 1954................................................................................... 244

6.56. Eötvös Competition 1955................................................................................... 244

6.57. Eötvös Competition 1957................................................................................... 244

6.58. Eötvös Competition 1958................................................................................... 245

6.59. Eötvös Competition 1959................................................................................... 245

6.60. Eötvös Competition 1960................................................................................... 245

6.61. Eötvös Competition 1961................................................................................... 246

6.62. Eötvös Competition 1962................................................................................... 246

6.63. Eötvös Competition 1963................................................................................... 246

6.64. Eötvös Competition 1964................................................................................... 247

6.65. Eötvös Competition 1965................................................................................... 247

6.66. Eötvös Competition 1966................................................................................... 247

6.67. Eötvös Competition 1967................................................................................... 248

6.68. Eötvös Competition 1968................................................................................... 248

6.69. Eötvös Competition 1969................................................................................... 248

6.70. Eötvös Competition 1970................................................................................... 249

6.71. Eötvös Competition 1971................................................................................... 249

6.72. Eötvös Competition 1972................................................................................... 249

6.73. Eötvös Competition 1973................................................................................... 250

6.74. Eötvös Competition 1974................................................................................... 250

6.75. Eötvös Competition 1975................................................................................... 250

6.76. Eötvös Competition 1976................................................................................... 251

6.77. Eötvös Competition 1977................................................................................... 251

6.78. Eötvös Competition 1978................................................................................... 251

6.79. Eötvös Competition 1979................................................................................... 252

6.80. Eötvös Competition 1980................................................................................... 252

6.81. Eötvös Competition 1981................................................................................... 252

6.82. Eötvös Competition 1982................................................................................... 253

6.83. Eötvös Competition 1983................................................................................... 253

6.84. Eötvös Competition 1984................................................................................... 253

6.85. Eötvös Competition 1985................................................................................... 254

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6.86. Eötvös Competition 1986................................................................................... 254

6.87. Eötvös Competition 1987................................................................................... 254

6.88. Eötvös Competition 1988................................................................................... 255

6.89. Eötvös Competition 1989................................................................................... 255

6.90. Eötvös Competition 1990................................................................................... 255

6.91. Eötvös Competition 1991................................................................................... 256

6.92. Eötvös Competition 1992................................................................................... 256

6.93. Eötvös Competition 1993................................................................................... 256

6.94. Eötvös Competition 1994................................................................................... 257

6.95. Eötvös Competition 1995................................................................................... 257

6.96. Eötvös Competition 1996................................................................................... 257

6.97. Eötvös Competition 1997................................................................................... 258

6.98. Eötvös Competition 1998................................................................................... 258

6.99. Eötvös Competition 1999................................................................................... 258

6.100. Eötvös Competition 2000................................................................................. 258

6.101. Eötvös Competition 2001................................................................................. 259

6.102. Eötvös Competition 2002................................................................................. 259

7. INMO (1995 – 2004) ................................................................................................... 260

7.1. INMO 1995 .......................................................................................................... 261

7.2. INMO 1996 .......................................................................................................... 262

7.3. INMO 1997 .......................................................................................................... 263

7.4. INMO 1998 .......................................................................................................... 264

7.5. INMO 1999 .......................................................................................................... 265

7.6. INMO 2000 .......................................................................................................... 266

7.7. INMO 2001 .......................................................................................................... 267

7.8. INMO 2002 .......................................................................................................... 268

7.9. INMO 2003 .......................................................................................................... 269

7.10. INMO 2004 ........................................................................................................ 270

8. Irish (1988 – 2003) ...................................................................................................... 271

8.1. Irish 1988.............................................................................................................. 272

8.2. Irish 1989.............................................................................................................. 273

8.3. Irish 1990.............................................................................................................. 274

8.4. Irish 1991.............................................................................................................. 275

8.5. Irish 1992.............................................................................................................. 276

8.6. Irish 1993.............................................................................................................. 277

8.7. Irish 1994.............................................................................................................. 278

8.8. Irish 1995.............................................................................................................. 279

8.9. Irish 1996.............................................................................................................. 280

8.10. Irish 1997............................................................................................................ 281

8.11. Irish 1998............................................................................................................ 282

8.12. Irish 1999............................................................................................................ 283

8.13. Irish 2000............................................................................................................ 284

8.14. Irish 2001............................................................................................................ 285

8.15. Irish 2002............................................................................................................ 286

8.16. Irish 2003............................................................................................................ 287

9. Mexican (1987 – 2003) ................................................................................................ 288

9.1. Mexican 1987 ....................................................................................................... 289

9.2. Mexican 1988 ....................................................................................................... 290

9.3. Mexican 1989 ....................................................................................................... 291

9.4. Mexican 1990 ....................................................................................................... 292

9.5. Mexican 1991 ....................................................................................................... 293

9.6. Mexican 1992 ....................................................................................................... 294

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9.7. Mexican 1993 ....................................................................................................... 295

9.8. Mexican 1994 ....................................................................................................... 296

9.9. Mexican 1995 ....................................................................................................... 297

9.10. Mexican 1996 ..................................................................................................... 298

9.11. Mexican 1997 ..................................................................................................... 299

9.12. Mexican 1998 ..................................................................................................... 300

9.13. Mexican 1999 ..................................................................................................... 301

9.14. Mexican 2000 ..................................................................................................... 302

9.15. Mexican 2001 ..................................................................................................... 303

9.16. Mexican 2003 ..................................................................................................... 304

9.17. Mexican 2004 ..................................................................................................... 305

10. Polish (1983 – 2003) .................................................................................................. 306

10.1. Polish 1983 ......................................................................................................... 307

10.2. Polish 1984 ......................................................................................................... 308

10.3. Polish 1985 ......................................................................................................... 309

10.4. Polish 1986 ......................................................................................................... 310

10.5. Polish 1987 ......................................................................................................... 311

10.6. Polish 1988 ......................................................................................................... 312

10.7. Polish 1989 ......................................................................................................... 313

10.8. Polish 1990 ......................................................................................................... 314

10.9. Polish 1991 ......................................................................................................... 315

10.10. Polish 1992 ....................................................................................................... 316

10.11. Polish 1993 ....................................................................................................... 317

10.12. Polish 1994 ....................................................................................................... 318

10.13. Polish 1995 ....................................................................................................... 319

10.14. Polish 1996 ....................................................................................................... 320

10.15. Polish 1997 ....................................................................................................... 321

10.16. Polish 1998 ....................................................................................................... 322

10.17. Polish 1999 ....................................................................................................... 323

10.18. Polish 2000 ....................................................................................................... 324

10.19. Polish 2001 ....................................................................................................... 325

10.20. Polish 2002 ....................................................................................................... 326

10.21. Polish 2003 ....................................................................................................... 327

11. Spanish (1990 – 2003) ............................................................................................... 328

11.1. Spanish 1990 ...................................................................................................... 329

11.2. Spanish 1991 ...................................................................................................... 330

11.3. Spanish 1992 ...................................................................................................... 331

11.4. Spanish 1993 ...................................................................................................... 332

11.5. Spanish 1994 ...................................................................................................... 333

11.6. Spanish 1995 ...................................................................................................... 334

11.7. Spanish 1996 ...................................................................................................... 335

11.8. Spanish 1997 ...................................................................................................... 336

11.9. Spanish 1998 ...................................................................................................... 337

11.10. Spanish 1999 .................................................................................................... 338

11.11. Spanish 2000 .................................................................................................... 339

11.12. Spanish 2001 .................................................................................................... 340

11.13. Spanish 2002 .................................................................................................... 341

11.14. Spanish 2003 .................................................................................................... 342

12. Swedish (1961 – 2003) ............................................................................................... 343

12.1. Swedish 1961 ..................................................................................................... 344

12.2. Swedish 1962 ..................................................................................................... 345

12.3. Swedish 1963 ..................................................................................................... 346

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12.4. Swedish 1964 ..................................................................................................... 347

12.5. Swedish 1965 ..................................................................................................... 348

12.6. Swedish 1966 ..................................................................................................... 349

12.7. Swedish 1967 ..................................................................................................... 350

12.8. Swedish 1968 ..................................................................................................... 351

12.9. Swedish 1969 ..................................................................................................... 352

12.10. Swedish 1970.................................................................................................... 353

12.11. Swedish 1971.................................................................................................... 354

12.12. Swedish 1972.................................................................................................... 355

12.13. Swedish 1973.................................................................................................... 356

12.14. Swedish 1974.................................................................................................... 357

12.15. Swedish 1975.................................................................................................... 358

12.16. Swedish 1976.................................................................................................... 359

12.17. Swedish 1977.................................................................................................... 360

12.18. Swedish 1978.................................................................................................... 361

12.19. Swedish 1979.................................................................................................... 362

12.20. Swedish 980 ..................................................................................................... 363

12.21. Swedish 1981.................................................................................................... 364

12.22. Swedish 1982.................................................................................................... 365

12.23. Swedish 1983.................................................................................................... 366

12.24. Swedish 1984.................................................................................................... 367

12.25. Swedish 1985.................................................................................................... 368

12.26. Swedish 1986.................................................................................................... 369

12.27. Swedish 1987.................................................................................................... 370

12.28. Swedish 1988.................................................................................................... 371

12.29. Swedish 1989.................................................................................................... 372

12.30. Swedish 1990.................................................................................................... 373

12.31. Swedish 1991.................................................................................................... 374

12.32. Swedish 1992.................................................................................................... 375

12.33. Swedish 1993.................................................................................................... 376

12.34. Swedish 1994.................................................................................................... 377

12.35. Swedish 1995.................................................................................................... 378

12.36. Swedish 1996.................................................................................................... 379

12.37. Swedish 1997.................................................................................................... 380

12.38. Swedish 1998.................................................................................................... 381

12.39. Swedish 1999.................................................................................................... 382

12.40. Swedish 2000.................................................................................................... 383

12.41. Swedish 2001.................................................................................................... 384

12.42. Swedish 2002.................................................................................................... 385

12.43. Swedish 2003.................................................................................................... 386

13. USAMO (1972 – 2003) .............................................................................................. 387

13.1. USAMO 1972..................................................................................................... 388

13.2. USAMO 1973..................................................................................................... 389

13.3. USAMO 1974..................................................................................................... 390

13.4. USAMO 1975..................................................................................................... 391

13.5. USAMO 1976..................................................................................................... 392

13.6. USAMO 1977..................................................................................................... 393

13.7. USAMO 1978..................................................................................................... 394

13.8. USAMO 1979..................................................................................................... 395

13.9. USAMO 1980..................................................................................................... 396

13.10. USAMO 1981................................................................................................... 397

13.11. USAMO 1982................................................................................................... 398

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13.12. USAMO 1983................................................................................................... 399

13.13. USAMO 1984................................................................................................... 400

13.14. USAMO 1985................................................................................................... 401

13.15. USAMO 1986................................................................................................... 402

13.16. USAMO 1987................................................................................................... 403

13.17. USAMO 1988................................................................................................... 404

13.18. USAMO 1989................................................................................................... 405

13.19. USAMO 1990................................................................................................... 406

13.20. USAMO 1991................................................................................................... 407

13.21. USAMO 1992................................................................................................... 408

13.22. USAMO 1993................................................................................................... 409

13.23. USAMO 1994................................................................................................... 410

13.24. USAMO 1995................................................................................................... 411

13.25. USAMO 1996................................................................................................... 412

13.26. USAMO 1997................................................................................................... 413

13.27. USAMO 1998................................................................................................... 414

13.28. USAMO 1999................................................................................................... 415

13.29. USAMO 2000................................................................................................... 416

13.30. USAMO 2001................................................................................................... 417

13.31. USAMO 2002................................................................................................... 418

13.32. USAMO 2003................................................................................................... 419

14. Vietnam (1962 – 2003) .............................................................................................. 420

14.1. Vietnam 1962 ..................................................................................................... 421

14.2. Vietnam 1963 ..................................................................................................... 422

14.3. Vietnam 1964 ..................................................................................................... 423

14.4. Vietnam 1965 ..................................................................................................... 424

14.5. Vietnam 1966 ..................................................................................................... 425

14.6. Vietnam 1967 ..................................................................................................... 426

14.7. Vietnam 1968 ..................................................................................................... 427

14.8. Vietnam 1969 ..................................................................................................... 428

14.9. Vietnam 1970 ..................................................................................................... 429

14.10. Vietnam 1971 ................................................................................................... 430

14.11. Vietnam 1972 ................................................................................................... 431

14.12. Vietnam 1974 ................................................................................................... 432

14.13. Vietnam 1975 ................................................................................................... 433

14.14. Vietnam 1976 ................................................................................................... 434

14.15. Vietnam 1977 ................................................................................................... 435

14.16. Vietnam 1978 ................................................................................................... 436

14.17. Vietnam 1979 ................................................................................................... 437

14.18. Vietnam 1980 ................................................................................................... 438

14.19. Vietnam 1981 ................................................................................................... 439

14.20. Vietnam 1982 ................................................................................................... 440

14.21. Vietnam 1983 ................................................................................................... 441

14.22. Vietnam 1984 ................................................................................................... 442

14.23. Vietnam 1985 ................................................................................................... 443

14.24. Vietnam 1986 ................................................................................................... 444

14.25. Vietnam 1987 ................................................................................................... 445

14.26. Vietnam 1988 ................................................................................................... 446

14.27. Vietnam 1989 ................................................................................................... 447

14.28. Vietnam 1990 ................................................................................................... 448

14.29. Vietnam 1991 ................................................................................................... 449

14.30. Vietnam 1992 ................................................................................................... 450

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14.31. Vietnam 1993 ................................................................................................... 451

14.32. Vietnam 1994 ................................................................................................... 452

14.33. Vietnam 1995 ................................................................................................... 453

14.34. Vietnam 1996 ................................................................................................... 454

14.35. Vietnam 1997 ................................................................................................... 455

14.36. Vietnam 1998 ................................................................................................... 456

14.37. Vietnam 1999 ................................................................................................... 457

14.38. Vietnam 2000 ................................................................................................... 458

14.39. Vietnam 2001 ................................................................................................... 459

14.40. Vietnam 2002 ................................................................................................... 460

14.41. Vietnam 2003 ................................................................................................... 461

PART II. International/Regional Olympiad problems................................................ 462

15. Iberoamerican (1985 – 2003) .................................................................................... 462

15.1. Iberoamerican 1985............................................................................................ 463

15.2. Iberoamerican 1987............................................................................................ 464

15.3. Iberoamerican 1988............................................................................................ 465

15.4. Iberoamerican 1989............................................................................................ 466

15.5. Iberoamerican 1990............................................................................................ 467

15.6. Iberoamerican 1991............................................................................................ 468

15.7. Iberoamerican 1992............................................................................................ 469

15.8. Iberoamerican 1993............................................................................................ 470

15.9. Iberoamerican 1994............................................................................................ 471

15.10. Iberoamerican 1995.......................................................................................... 472

15.11. Iberoamerican 1996.......................................................................................... 473

15.12. Iberoamerican 1997.......................................................................................... 474

15.13. Iberoamerican 1998.......................................................................................... 475

15.14. Iberoamerican 1999.......................................................................................... 466

15.15. Iberoamerican 2000.......................................................................................... 477

15.16. Iberoamerican 2001.......................................................................................... 478

15.17. Iberoamerican 2002.......................................................................................... 479

15.18. Iberoamerican 2003.......................................................................................... 480

16. Balkan (1984 – 2003) ................................................................................................ 481

16.1. Balkan 1984........................................................................................................ 482

16.2. Balkan 1985........................................................................................................ 483

16.3. Balkan 1986........................................................................................................ 484

16.4. Balkan 1987........................................................................................................ 485

16.5. Balkan 1988........................................................................................................ 486

16.6. Balkan 1989........................................................................................................ 487

16.7. Balkan 1990........................................................................................................ 488

16.8. Balkan 1991........................................................................................................ 489

16.9. Balkan 1992........................................................................................................ 490

16.10. Balkan 1993...................................................................................................... 491

16.11. Balkan 1994...................................................................................................... 492

16.12. Balkan 1995...................................................................................................... 493

16.13. Balkan 1996...................................................................................................... 494

16.14. Balkan 1997...................................................................................................... 495

16.15. Balkan 1998...................................................................................................... 496

16.16. Balkan 1999...................................................................................................... 497

16.17. Balkan 2000...................................................................................................... 498

16.18. Balkan 2001...................................................................................................... 499

16.19. Balkan 2002...................................................................................................... 500

16.20. Balkan 2003...................................................................................................... 501

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17. Austrian – Polish (1978 – 2003) ................................................................................ 502

17.1. Austrian – Polish 1978 ....................................................................................... 503

17.2. Austrian – Polish 1979 ....................................................................................... 504

17.3. Austrian – Polish 1980 ....................................................................................... 505

17.4. Austrian – Polish 1981 ....................................................................................... 506

17.5. Austrian – Polish 1982 ....................................................................................... 507

17.6. Austrian – Polish 1983 ....................................................................................... 508

17.7. Austrian – Polish 1984 ....................................................................................... 509

17.8. Austrian – Polish 1985 ....................................................................................... 510

17.9. Austrian – Polish 1986 ....................................................................................... 511

17.10. Austrian – Polish 1987 ..................................................................................... 512

17.11. Austrian – Polish 1988 ..................................................................................... 513

17.12. Austrian – Polish 1989 ..................................................................................... 514

17.13. Austrian – Polish 1990 ..................................................................................... 515

17.14. Austrian – Polish 1991 ..................................................................................... 516

17.15. Austrian – Polish 1992 ..................................................................................... 517

17.16. Austrian – Polish 1993 ..................................................................................... 518

17.17. Austrian – Polish 1994 ..................................................................................... 519

17.18. Austrian – Polish 1995 ..................................................................................... 520

17.19. Austrian – Polish 1996 ..................................................................................... 521

17.20. Austrian – Polish 1997 ..................................................................................... 522

17.21. Austrian – Polish 1998 ..................................................................................... 523

17.22. Austrian – Polish 1999 ..................................................................................... 524

17.23. Austrian – Polish 2000 ..................................................................................... 525

17.24. Austrian – Polish 2001 ..................................................................................... 526

17.25. Austrian – Polish 2002 ..................................................................................... 527

17.26. Austrian – Polish 2003 ..................................................................................... 528

18. APMO (1989 – 2004) ................................................................................................. 529

18.1. APMO 1989 ....................................................................................................... 530

18.2. APMO 1990 ....................................................................................................... 531

18.3. APMO 1991 ....................................................................................................... 532

18.4. APMO 1992 ....................................................................................................... 533

18.5. APMO 1993 ....................................................................................................... 534

18.6. APMO 1994 ....................................................................................................... 535

18.7. APMO 1995 ....................................................................................................... 536

18.8. APMO 1996 ....................................................................................................... 537

18.9. APMO 1997 ....................................................................................................... 538

18.10. APMO 1998 ..................................................................................................... 539

18.11. APMO 1999 ..................................................................................................... 540

18.12. APMO 2000 ..................................................................................................... 541

18.13. APMO 2001 ..................................................................................................... 542

18.14. APMO 2002 ..................................................................................................... 543

18.15. APMO 2003 ..................................................................................................... 544

18.16. APMO 2004 ..................................................................................................... 545

19. IMO (1959 – 2003) .................................................................................................... 546

19.1. IMO 1959 ........................................................................................................... 547

19.2. IMO 1960 ........................................................................................................... 548

19.3. IMO 1961 ........................................................................................................... 549

19.4. IMO 1962 ........................................................................................................... 550

19.5. IMO 1963 ........................................................................................................... 551

19.6. IMO 1964 ........................................................................................................... 552

19.7. IMO 1965 ........................................................................................................... 553

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19.8. IMO 1966 ........................................................................................................... 554

19.9. IMO 1967 ........................................................................................................... 555

19.10. IMO 1968 ......................................................................................................... 556

19.11. IMO 1969 ......................................................................................................... 557

19.12. IMO 1970 ......................................................................................................... 558

19.13. IMO 1971 ......................................................................................................... 559

19.14. IMO 1972 ......................................................................................................... 560

19.15. IMO 1973 ......................................................................................................... 561

19.16. IMO 1974 ......................................................................................................... 562

19.17. IMO 1975 ......................................................................................................... 563

19.18. IMO 1976 ......................................................................................................... 564

19.19. IMO 1977 ......................................................................................................... 565

19.20. IMO 1978 ......................................................................................................... 566

19.21. IMO 1979 ......................................................................................................... 567

19.22. IMO 1981 ......................................................................................................... 568

19.23. IMO 1982 ......................................................................................................... 569

19.24. IMO 1983 ......................................................................................................... 570

19.25. IMO 1984 ......................................................................................................... 571

19.26. IMO 1985 ......................................................................................................... 572

19.27. IMO 1986 ......................................................................................................... 573

19.28. IMO 1987 ......................................................................................................... 574

19.29. IMO 1988 ......................................................................................................... 575

19.30. IMO 1989 ......................................................................................................... 576

19.31. IMO 1990 ......................................................................................................... 577

19.32. IMO 1991 ......................................................................................................... 578

19.33. IMO 1992 ......................................................................................................... 579

19.34. IMO 1993 ......................................................................................................... 580

19.35. IMO 1994 ......................................................................................................... 581

19.36. IMO 1995 ......................................................................................................... 582

19.37. IMO 1996 ......................................................................................................... 583

19.38. IMO 1997 ......................................................................................................... 584

19.39. IMO 1998 ......................................................................................................... 585

19.40. IMO 1999 ......................................................................................................... 586

19.41. IMO 2000 ......................................................................................................... 587

19.42. IMO 2001 ......................................................................................................... 588

19.43. IMO 2002 ......................................................................................................... 589

19.44. IMO 2003 ......................................................................................................... 590

20. Junior Balkan (1997 – 2003) .................................................................................... 591

20.1. Junior Balkan 1997............................................................................................. 592

20.2. Junior Balkan 1998............................................................................................. 593

20.3. Junior Balkan 1999............................................................................................. 594

20.4. Junior Balkan 2000............................................................................................. 595

20.5. Junior Balkan 2001............................................................................................. 596

20.6. Junior Balkan 2002............................................................................................. 597

20.7. Junior Balkan 2003............................................................................................. 598

21. Shortlist IMO (1959 – 2002) ..................................................................................... 599

21.1. Shortlist IMO 1959 – 1967 ................................................................................ 600

21.2. Shortlist IMO 1981............................................................................................. 602

21.3. Shortlist IMO 1982............................................................................................. 603

21.4. Shortlist IMO 1983............................................................................................. 604

21.5. Shortlist IMO 1984............................................................................................. 606

21.6. Shortlist IMO 1985............................................................................................. 608

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21.7. Shortlist IMO 1986............................................................................................. 610

21.8. Shortlist IMO 1987............................................................................................. 612

21.9. Shortlist IMO 1988............................................................................................. 614

21.10. Shortlist IMO 1989........................................................................................... 616

21.11. Shortlist IMO 1990........................................................................................... 618

21.12. Shortlist IMO 1991........................................................................................... 620

21.13. Shortlist IMO 1992........................................................................................... 623

21.14. Shortlist IMO 1993........................................................................................... 624

21.15. Shortlist IMO 1994........................................................................................... 626

21.16. Shortlist IMO 1995........................................................................................... 628

21.17. Shortlist IMO 1996........................................................................................... 630

21.18. Shortlist IMO 1997........................................................................................... 632

21.19. Shortlist IMO 1998........................................................................................... 634

21.20. Shortlist IMO 1999........................................................................................... 636

21.21. Shortlist IMO 2000........................................................................................... 638

21.22. Shortlist IMO 2001........................................................................................... 641

21.22. Shortlist IMO 2002........................................................................................... 643

22. OMCC (1999 – 2003) ................................................................................................. 645

22.1. OMCC 1999 ....................................................................................................... 646

22.2. OMCC 2000 ....................................................................................................... 647

22.3. OMCC 2001 ....................................................................................................... 648

22.4. OMCC 2002 ....................................................................................................... 649

22.5. OMCC 2003 ....................................................................................................... 650

23. PUTNAM (1938 – 2003) ............................................................................................ 651

23.1. PUTNAM 1938 .................................................................................................. 652

23.2. PUTNAM 1939 .................................................................................................. 654

23.3. PUTNAM 1940 .................................................................................................. 656

23.4. PUTNAM 1941 .................................................................................................. 657

23.5. PUTNAM 1942 .................................................................................................. 659

23.6. PUTNAM 1946 .................................................................................................. 660

23.7. PUTNAM 1947 .................................................................................................. 661

23.8. PUTNAM 1948 .................................................................................................. 662

23.9. PUTNAM 1949 .................................................................................................. 663

23.10. PUTNAM 1950 ................................................................................................ 664

23.11. PUTNAM 1951 ................................................................................................ 666

23.12. PUTNAM 1952 ................................................................................................ 667

23.13. PUTNAM 1953 ................................................................................................ 668

23.14. PUTNAM 1954 ................................................................................................ 669

23.15. PUTNAM 1955 ................................................................................................ 670

23.16. PUTNAM 1956 ................................................................................................ 671

23.17. PUTNAM 1957 ................................................................................................ 672

23.18. PUTNAM 1958 ................................................................................................ 673

23.19. PUTNAM 1959 ................................................................................................ 675

23.20. PUTNAM 1960 ................................................................................................ 677

23.21. PUTNAM 1961 ................................................................................................ 678

23.22. PUTNAM 1962 ................................................................................................ 679

23.23. PUTNAM 1963 ................................................................................................ 680

23.24. PUTNAM 1964 ................................................................................................ 681

23.25. PUTNAM 1965 ................................................................................................ 682

23.26. PUTNAM 1966 ................................................................................................ 683

23.27. PUTNAM 1967 ................................................................................................ 684

23.28. PUTNAM 1968 ................................................................................................ 685