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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 650 · 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 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 103 (b) 104 (c) 112 (d) 94
  2. 2.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 436 (c) 362 (d) 435
  3. 3.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) 54 (b) 162 (c) 18 (d) 57
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 20 (b) 9 (c) 18 (d) 19
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 18 (b) 19 (c) 9 (d) 16
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 1 (b) 2 (c) 4 (d) 3
  7. 7.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4
  8. 8.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) 72 (c) 8 (d) 24
  9. 9.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  10. 10.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) 63 (c) 7 (d) 24
  11. 11.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 9 (d) 10
  13. 13.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 538 (b) 430 (c) 528 (d) 537
  14. 14.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 577 (c) 456 (d) 576
  15. 15.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 270 (c) 258 (d) 279
  16. 16.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) 69 (b) 66 (c) 198 (d) 22
  17. 17.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  18. 18.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  19. 19.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 68 (c) 76 (d) 67
  20. 20.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 6 (d) 10
  21. 21.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 75 (c) 84 (d) 66
  22. 22.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 529 (b) 424 (c) 528 (d) 519
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 15 (b) 14 (c) 5 (d) 16
  24. 24.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) 21 (b) 18 (c) 54 (d) 6
  25. 25.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 2 (b) 4 (c) 1 (d) 3
  27. 27.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 525 (c) 422 (d) 526
  28. 28.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
  29. 29.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 69 (c) 23 (d) 72
  30. 30.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 70 (c) 52 (d) 61
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 18 (b) 16 (c) 17 (d) 7
  32. 32.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) 189 (b) 21 (c) 66 (d) 63
  33. 33.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 121 (b) 130 (c) 122 (d) 112
  34. 34.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 64 (c) 82 (d) 73
  35. 35.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 15 (c) 45 (d) 135
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 5 (b) 2 (c) 3 (d) 4
  37. 37.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  38. 38.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 59 (c) 50 (d) 68
  39. 39.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) 30 (b) 33 (c) 10 (d) 90
  40. 40.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4

Answer key

  1. 103
  2. 435
  3. 54
  4. 19
  5. 18
  6. 3
  7. 3
  8. 24
  9. 6
  10. 21
  11. 2
  12. 9
  13. 537
  14. 576
  15. 279
  16. 66
  17. 7
  18. 3
  19. 67
  20. 5
  21. 75
  22. 528
  23. 15
  24. 18
  25. 4
  26. 3
  27. 525
  28. 8
  29. 69
  30. 61
  31. 17
  32. 63
  33. 121
  34. 73
  35. 45
  36. 4
  37. 7
  38. 59
  39. 30
  40. 5

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