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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 595 · 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.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) 10 (b) 33 (c) 30 (d) 90
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 6 (b) 5 (c) 7 (d) 4
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 2 (b) 4 (c) 3 (d) 5
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 10 (d) 2
  5. 5.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 102 (c) 112 (d) 111
  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) 24 (b) 27 (c) 72 (d) 8
  7. 7.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  8. 8.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) 30 (c) 81 (d) 9
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 4 (b) 7 (c) 5 (d) 6
  10. 10.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 32 (c) 41 (d) 42
  11. 11.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
  12. 12.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  13. 13.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) 7 (b) 63 (c) 24 (d) 21
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 9 (d) 19
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 3 (b) 15 (c) 14 (d) 13
  16. 16.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 76 (c) 94 (d) 85
  17. 17.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  18. 18.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) 198 (b) 66 (c) 22 (d) 69
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 4 (b) 5 (c) 7 (d) 6
  20. 20.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 404 (c) 499 (d) 489
  21. 21.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) 60 (c) 57 (d) 19
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 3 (b) 9 (c) 11 (d) 10
  23. 23.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 131 (c) 140 (d) 122
  24. 24.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 7 (d) 9
  25. 25.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 133 (c) 124 (d) 142
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 7 (b) 3 (c) 6 (d) 4
  27. 27.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) 66 (c) 63 (d) 189
  28. 28.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 326 (b) 381 (c) 382 (d) 372
  29. 29.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 4 (d) 6
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 20 (b) 19 (c) 8 (d) 18
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  32. 32.The numbers 14 to 22 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) 162 (c) 54 (d) 57
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 4 (b) 7 (c) 6 (d) 5
  34. 34.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 3 (b) 5 (c) 2 (d) 4
  36. 36.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 516 (c) 526 (d) 422
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 19 (b) 18 (c) 9 (d) 20
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 93? (a) 9 (b) 19 (c) 20 (d) 18
  39. 39.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) 45 (b) 126 (c) 14 (d) 42
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 6 (b) 18 (c) 16 (d) 17

Answer key

  1. 30
  2. 6
  3. 4
  4. 3
  5. 111
  6. 24
  7. 3
  8. 27
  9. 6
  10. 41
  11. 9
  12. 4
  13. 21
  14. 19
  15. 14
  16. 85
  17. 9
  18. 66
  19. 6
  20. 498
  21. 57
  22. 10
  23. 131
  24. 8
  25. 133
  26. 6
  27. 63
  28. 381
  29. 5
  30. 19
  31. 2
  32. 54
  33. 6
  34. 7
  35. 4
  36. 525
  37. 19
  38. 19
  39. 42
  40. 17

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