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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 866 · 40 questions
TalentJR

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

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  1. 1.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 152 (c) 170 (d) 161
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 12 (b) 14 (c) 3 (d) 13
  3. 3.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 90 (c) 30 (d) 10
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  5. 5.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  6. 6.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 24 (c) 8 (d) 27
  7. 7.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 14 (c) 45 (d) 42
  8. 8.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 108 (c) 36 (d) 39
  9. 9.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 324 (c) 216 (d) 217
  10. 10.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3
  11. 11.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 20 (b) 21 (c) 9 (d) 19
  13. 13.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 84 (c) 83 (d) 92
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 19 (b) 7 (c) 17 (d) 18
  15. 15.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 288 (c) 289 (d) 264
  16. 16.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  17. 17.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 75 (c) 24 (d) 72
  18. 18.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  19. 19.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 17 (c) 54 (d) 51
  20. 20.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 186 (c) 178 (d) 177
  21. 21.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 420 (c) 358 (d) 429
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 18 (b) 16 (c) 6 (d) 17
  23. 23.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 262 (c) 286 (d) 276
  24. 24.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  25. 25.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 195 (c) 186 (d) 202
  26. 26.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 284 (b) 318 (c) 309 (d) 319
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 20 (d) 19
  29. 29.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 111 (b) 112 (c) 102 (d) 120
  30. 30.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 388 (c) 387 (d) 330
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 94? (a) 15 (b) 14 (c) 12 (d) 9
  32. 32.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 358 (c) 348 (d) 357
  33. 33.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 16 (c) 48 (d) 51
  34. 34.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 321 (c) 312 (d) 322
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 17 (b) 5 (c) 16 (d) 15
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 1 (b) 2 (c) 4 (d) 3
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 13 (b) 7 (c) 12 (d) 10
  38. 38.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 9 (c) 81 (d) 30
  39. 39.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 6 (c) 54 (d) 21
  40. 40.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 220 (c) 218 (d) 210

Answer key

  1. 161
  2. 13
  3. 30
  4. 3
  5. 5
  6. 24
  7. 42
  8. 36
  9. 216
  10. 4
  11. 7
  12. 20
  13. 83
  14. 18
  15. 288
  16. 9
  17. 72
  18. 6
  19. 51
  20. 177
  21. 429
  22. 17
  23. 285
  24. 9
  25. 195
  26. 318
  27. 2
  28. 20
  29. 111
  30. 387
  31. 14
  32. 357
  33. 48
  34. 321
  35. 16
  36. 3
  37. 12
  38. 27
  39. 18
  40. 219

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