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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 137 · 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 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 75 (c) 66 (d) 76
  2. 2.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) 30 (c) 90 (d) 33
  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) 162 (b) 57 (c) 54 (d) 18
  4. 4.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 36 (c) 39 (d) 12
  5. 5.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 42 (c) 52 (d) 51
  6. 6.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  7. 7.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 156 (c) 147 (d) 138
  8. 8.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 133 (b) 124 (c) 134 (d) 142
  9. 9.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 86 (c) 104 (d) 96
  10. 10.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 3 (b) 4 (c) 1 (d) 2
  12. 12.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 31 (b) 32 (c) 40 (d) 22
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 19 (b) 18 (c) 20 (d) 9
  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) 577 (b) 576 (c) 567 (d) 456
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 6 (b) 5 (c) 4 (d) 7
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 2 (b) 5 (c) 4 (d) 3
  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) 27 (b) 72 (c) 8 (d) 24
  18. 18.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) 27 (d) 30
  19. 19.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) 98 (c) 89 (d) 90
  20. 20.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 80 (c) 62 (d) 71
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 2 (b) 4 (c) 3 (d) 5
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 5 (b) 6 (c) 4 (d) 3
  23. 23.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 628 (c) 618 (d) 490
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 5 (b) 4 (c) 7 (d) 6
  25. 25.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  26. 26.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 6 (b) 4 (c) 3 (d) 5
  28. 28.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 146 (c) 156 (d) 155
  29. 29.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 110 (c) 100 (d) 109
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 17 (b) 19 (c) 18 (d) 8
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 20 (b) 18 (c) 19 (d) 8
  32. 32.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 137 (b) 138 (c) 146 (d) 128
  33. 33.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) 57 (b) 60 (c) 19 (d) 171
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 6 (b) 4 (c) 5 (d) 3
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 7 (b) 4 (c) 5 (d) 6
  36. 36.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 397 (c) 387 (d) 336
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 54? (a) 15 (b) 17 (c) 5 (d) 16
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 4 (d) 3
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 5 (b) 4 (c) 7 (d) 6
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 14 (b) 15 (c) 4 (d) 16

Answer key

  1. 75
  2. 30
  3. 54
  4. 36
  5. 51
  6. 7
  7. 147
  8. 133
  9. 95
  10. 5
  11. 3
  12. 31
  13. 19
  14. 576
  15. 6
  16. 4
  17. 24
  18. 27
  19. 89
  20. 71
  21. 4
  22. 5
  23. 627
  24. 6
  25. 4
  26. 3
  27. 5
  28. 155
  29. 109
  30. 18
  31. 19
  32. 137
  33. 57
  34. 5
  35. 6
  36. 396
  37. 16
  38. 3
  39. 6
  40. 15

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