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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 152 · 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.

NameDateTime takenScore ___ / 40
  1. 1.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  2. 2.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 493 (c) 492 (d) 400
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 16 (b) 14 (c) 4 (d) 15
  4. 4.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 166 (c) 158 (d) 157
  5. 5.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 122 (c) 113 (d) 104
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  7. 7.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 171 (c) 19 (d) 57
  8. 8.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 198 (c) 69 (d) 66
  9. 9.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) 54 (b) 18 (c) 6 (d) 21
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 18 (b) 17 (c) 6 (d) 16
  11. 11.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 213 (c) 204 (d) 214
  12. 12.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) 14 (b) 42 (c) 126 (d) 45
  13. 13.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  14. 14.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
  15. 15.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 39 (c) 42 (d) 117
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 80? (a) 8 (b) 19 (c) 18 (d) 17
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 19 (b) 20 (c) 21 (d) 9
  18. 18.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) 90 (b) 30 (c) 33 (d) 10
  19. 19.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
  20. 20.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  22. 22.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 448 (c) 370 (d) 447
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 9 (b) 7 (c) 8 (d) 6
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 12 (b) 11 (c) 13 (d) 3
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 8 (b) 11 (c) 9 (d) 12
  26. 26.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 164 (c) 173 (d) 182
  27. 27.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  28. 28.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  29. 29.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 103 (b) 112 (c) 94 (d) 104
  30. 30.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 507 (c) 410 (d) 508
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 99? (a) 9 (b) 19 (c) 21 (d) 20
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 2 (b) 5 (c) 4 (d) 3
  33. 33.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 83 (c) 84 (d) 74
  34. 34.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 446 (b) 552 (c) 562 (d) 561
  35. 35.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) 27 (b) 24 (c) 72 (d) 8
  36. 36.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 520 (c) 510 (d) 519
  37. 37.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 68 (c) 77 (d) 78
  38. 38.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
  39. 39.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 142 (c) 134 (d) 133
  40. 40.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3

Answer key

  1. 8
  2. 492
  3. 15
  4. 157
  5. 113
  6. 2
  7. 57
  8. 66
  9. 18
  10. 17
  11. 213
  12. 42
  13. 7
  14. 9
  15. 39
  16. 18
  17. 20
  18. 30
  19. 3
  20. 5
  21. 7
  22. 447
  23. 8
  24. 12
  25. 11
  26. 173
  27. 3
  28. 4
  29. 103
  30. 507
  31. 20
  32. 4
  33. 83
  34. 561
  35. 24
  36. 519
  37. 77
  38. 51
  39. 133
  40. 4

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