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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 23 · 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 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 462 (c) 471 (d) 386
  2. 2.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 193 (b) 200 (c) 192 (d) 183
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 10 (d) 7
  4. 4.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 114 (c) 123 (d) 124
  5. 5.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  6. 6.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) 33 (b) 10 (c) 30 (d) 90
  7. 7.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 453 (c) 463 (d) 380
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 2 (b) 1 (c) 3 (d) 4
  9. 9.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 4 (d) 2
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  11. 11.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 9 (d) 7
  12. 12.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
  13. 13.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 7 (d) 14
  14. 14.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 109 (b) 110 (c) 100 (d) 118
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 16 (b) 13 (c) 15 (d) 9
  16. 16.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  17. 17.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) 27 (c) 30 (d) 9
  18. 18.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 92 (c) 91 (d) 100
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 6 (b) 3 (c) 4 (d) 5
  20. 20.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) 18 (b) 54 (c) 21 (d) 6
  21. 21.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 505 (b) 408 (c) 504 (d) 495
  22. 22.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 130 (c) 122 (d) 121
  23. 23.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 69 (b) 70 (c) 60 (d) 78
  24. 24.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 430 (b) 420 (c) 429 (d) 358
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  26. 26.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 162 (c) 171 (d) 180
  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) 68 (c) 76 (d) 58
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 70? (a) 18 (b) 16 (c) 7 (d) 17
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 21 (b) 9 (c) 20 (d) 19
  30. 30.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 37 (b) 28 (c) 46 (d) 38
  31. 31.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) 126 (c) 42 (d) 45
  32. 32.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  33. 33.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  34. 34.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 619 (c) 618 (d) 484
  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) 15 (b) 45 (c) 48 (d) 135
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 15 (b) 16 (c) 14 (d) 4
  37. 37.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 16 (b) 5 (c) 15 (d) 17
  39. 39.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 24 (c) 72 (d) 216
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 15 (b) 13 (c) 14 (d) 3

Answer key

  1. 471
  2. 192
  3. 6
  4. 123
  5. 3
  6. 30
  7. 462
  8. 3
  9. 3
  10. 8
  11. 8
  12. 4
  13. 6
  14. 109
  15. 15
  16. 7
  17. 27
  18. 91
  19. 5
  20. 18
  21. 504
  22. 121
  23. 69
  24. 429
  25. 2
  26. 171
  27. 67
  28. 17
  29. 20
  30. 37
  31. 42
  32. 9
  33. 2
  34. 618
  35. 45
  36. 15
  37. 7
  38. 16
  39. 72
  40. 14

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