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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 679 · 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 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) 24 (c) 63 (d) 21
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 15 (b) 14 (c) 13 (d) 3
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  4. 4.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) 87 (d) 96
  5. 5.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 422 (b) 526 (c) 516 (d) 525
  6. 6.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 34 (c) 43 (d) 44
  7. 7.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) 66 (b) 22 (c) 198 (d) 69
  8. 8.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 310 (c) 357 (d) 358
  9. 9.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 36 (c) 33 (d) 11
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  11. 11.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
  12. 12.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) 117 (b) 42 (c) 13 (d) 39
  13. 13.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 54 (c) 63 (d) 64
  14. 14.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 571 (b) 561 (c) 452 (d) 570
  15. 15.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 117 (c) 118 (d) 126
  16. 16.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) 51 (c) 17 (d) 54
  17. 17.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) 72 (b) 8 (c) 27 (d) 24
  18. 18.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 4 (b) 1 (c) 2 (d) 3
  20. 20.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) 45 (c) 126 (d) 42
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 53? (a) 14 (b) 16 (c) 5 (d) 15
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 4 (b) 5 (c) 7 (d) 6
  23. 23.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
  24. 24.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) 135 (d) 45
  25. 25.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  26. 26.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 15 (d) 5
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 63? (a) 5 (b) 7 (c) 4 (d) 6
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 2 (b) 4 (c) 3 (d) 5
  29. 29.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 430 (c) 538 (d) 537
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 12 (b) 14 (c) 3 (d) 13
  31. 31.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 116 (c) 106 (d) 115
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 4 (b) 1 (c) 3 (d) 2
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 6 (b) 4 (c) 5 (d) 3
  34. 34.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) 81 (b) 9 (c) 30 (d) 27
  35. 35.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 66? (a) 4 (b) 6 (c) 5 (d) 7
  37. 37.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  38. 38.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) 18 (d) 21
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 2 (b) 4 (c) 1 (d) 3
  40. 40.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1

Answer key

  1. 21
  2. 14
  3. 5
  4. 87
  5. 525
  6. 43
  7. 66
  8. 357
  9. 33
  10. 3
  11. 57
  12. 39
  13. 63
  14. 570
  15. 117
  16. 51
  17. 24
  18. 9
  19. 3
  20. 42
  21. 15
  22. 6
  23. 4
  24. 45
  25. 3
  26. 5
  27. 6
  28. 4
  29. 537
  30. 13
  31. 115
  32. 3
  33. 5
  34. 27
  35. 7
  36. 6
  37. 6
  38. 18
  39. 3
  40. 2

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