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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 305 · 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.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 592 (c) 466 (d) 582
  2. 2.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 7 (b) 18 (c) 16 (d) 17
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 12 (b) 14 (c) 15 (d) 7
  5. 5.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 5 (b) 17 (c) 15 (d) 16
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 20 (b) 19 (c) 21 (d) 9
  8. 8.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) 39 (b) 13 (c) 42 (d) 117
  9. 9.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) 447 (c) 370 (d) 448
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 8 (d) 9
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 3 (b) 6 (c) 4 (d) 5
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 98? (a) 19 (b) 9 (c) 21 (d) 20
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 43? (a) 3 (b) 2 (c) 5 (d) 4
  14. 14.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 62 (c) 61 (d) 70
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 9 (b) 8 (c) 6 (d) 7
  16. 16.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 152 (c) 142 (d) 151
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 3 (b) 5 (c) 4 (d) 2
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 16 (b) 17 (c) 5 (d) 15
  19. 19.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) 171 (b) 19 (c) 60 (d) 57
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 3 (b) 6 (c) 5 (d) 4
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 9 (b) 18 (c) 20 (d) 19
  22. 22.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 290 (c) 318 (d) 328
  23. 23.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 6 (b) 7 (c) 8 (d) 5
  25. 25.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 43 (c) 34 (d) 52
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 14 (b) 4 (c) 15 (d) 16
  27. 27.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 67 (b) 58 (c) 68 (d) 76
  28. 28.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 88 (c) 96 (d) 87
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 20 (d) 9
  31. 31.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 15 (c) 18 (d) 5
  32. 32.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 89 (c) 98 (d) 80
  33. 33.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
  34. 34.The numbers 17 to 25 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) 63 (c) 189 (d) 66
  35. 35.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 582 (c) 583 (d) 460
  36. 36.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 567 (c) 450 (d) 558
  37. 37.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) 102 (c) 112 (d) 120
  38. 38.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 5 (b) 4 (c) 6 (d) 3
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 16 (b) 15 (c) 5 (d) 14

Answer key

  1. 591
  2. 3
  3. 17
  4. 14
  5. 5
  6. 16
  7. 20
  8. 39
  9. 447
  10. 8
  11. 5
  12. 20
  13. 4
  14. 61
  15. 8
  16. 151
  17. 4
  18. 16
  19. 57
  20. 5
  21. 19
  22. 327
  23. 5
  24. 7
  25. 43
  26. 15
  27. 67
  28. 87
  29. 9
  30. 20
  31. 15
  32. 89
  33. 24
  34. 63
  35. 582
  36. 567
  37. 111
  38. 9
  39. 5
  40. 15

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