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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 846 · 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 times is the digit 3 written when you write all the numbers from 1 to 88? (a) 18 (b) 8 (c) 20 (d) 19
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 8 (b) 5 (c) 6 (d) 7
  3. 3.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4
  4. 4.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 102 (c) 110 (d) 101
  5. 5.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
  6. 6.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 98 (c) 107 (d) 108
  7. 7.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 124 (c) 115 (d) 116
  8. 8.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) 6 (c) 21 (d) 18
  9. 9.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 396 (c) 336 (d) 397
  10. 10.The numbers 16 to 24 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) 63 (c) 180 (d) 20
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 19 (b) 7 (c) 18 (d) 17
  12. 12.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 595 (c) 594 (d) 468
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 10 (b) 9 (c) 5 (d) 7
  14. 14.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 315 (c) 282 (d) 316
  15. 15.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 57 (c) 48 (d) 58
  16. 16.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  17. 17.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) 45 (c) 14 (d) 42
  18. 18.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 6 (b) 5 (c) 8 (d) 7
  20. 20.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 3 (b) 6 (c) 7 (d) 4
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 15 (b) 17 (c) 5 (d) 16
  23. 23.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 90 (c) 98 (d) 89
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 3 (b) 4 (c) 2 (d) 5
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 4 (b) 14 (c) 15 (d) 16
  26. 26.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 72 (c) 63 (d) 64
  27. 27.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 73 (c) 74 (d) 64
  28. 28.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 166 (c) 156 (d) 165
  29. 29.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 24 (c) 63 (d) 7
  30. 30.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  31. 31.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  32. 32.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 304 (c) 348 (d) 339
  33. 33.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 3 (b) 15 (c) 14 (d) 13
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 82? (a) 7 (b) 6 (c) 9 (d) 8
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 5 (b) 4 (c) 3 (d) 2
  37. 37.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) 8 (c) 24 (d) 72
  38. 38.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 117 (b) 118 (c) 108 (d) 126
  39. 39.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 4 (d) 6
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 6 (b) 7 (c) 4 (d) 5

Answer key

  1. 19
  2. 7
  3. 3
  4. 101
  5. 9
  6. 107
  7. 115
  8. 18
  9. 396
  10. 60
  11. 18
  12. 594
  13. 9
  14. 315
  15. 57
  16. 8
  17. 42
  18. 4
  19. 7
  20. 9
  21. 6
  22. 16
  23. 89
  24. 4
  25. 15
  26. 63
  27. 73
  28. 165
  29. 21
  30. 2
  31. 5
  32. 348
  33. 7
  34. 14
  35. 8
  36. 4
  37. 24
  38. 117
  39. 5
  40. 6

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