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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 645 · 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.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 9 (b) 20 (c) 19 (d) 21
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 1 (b) 2 (c) 3 (d) 4
  3. 3.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 362 (b) 426 (c) 436 (d) 435
  4. 4.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 10 (d) 9
  5. 5.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) 54 (c) 57 (d) 18
  6. 6.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 184 (c) 174 (d) 183
  7. 7.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  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) 30 (b) 81 (c) 27 (d) 9
  9. 9.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 408 (c) 504 (d) 505
  10. 10.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 68? (a) 6 (b) 7 (c) 5 (d) 4
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
  13. 13.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 87 (c) 88 (d) 78
  14. 14.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 101 (b) 110 (c) 92 (d) 102
  15. 15.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) 69 (c) 198 (d) 22
  16. 16.The numbers 12 to 20 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) 144 (c) 16 (d) 51
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 88? (a) 18 (b) 8 (c) 17 (d) 19
  18. 18.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 93 (c) 102 (d) 84
  19. 19.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 258 (c) 268 (d) 250
  20. 20.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
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 18 (b) 16 (c) 17 (d) 6
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 9 (b) 18 (c) 20 (d) 19
  23. 23.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) 23 (b) 207 (c) 72 (d) 69
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 4 (b) 14 (c) 16 (d) 15
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 82? (a) 6 (b) 9 (c) 8 (d) 7
  26. 26.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
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 19 (b) 17 (c) 18 (d) 8
  28. 28.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
  29. 29.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) 6 (c) 54 (d) 21
  30. 30.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 500 (b) 642 (c) 633 (d) 643
  31. 31.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 298 (c) 297 (d) 288
  32. 32.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 4 (b) 3 (c) 5 (d) 2
  34. 34.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 52? (a) 5 (b) 4 (c) 6 (d) 3
  36. 36.The numbers 1 to 9 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) 18 (c) 5 (d) 45
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 5 (b) 3 (c) 6 (d) 4
  38. 38.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) 100 (c) 109 (d) 110
  39. 39.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  40. 40.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) 63 (b) 7 (c) 21 (d) 24

Answer key

  1. 20
  2. 3
  3. 435
  4. 9
  5. 54
  6. 183
  7. 3
  8. 27
  9. 504
  10. 4
  11. 6
  12. 5
  13. 87
  14. 101
  15. 66
  16. 48
  17. 18
  18. 93
  19. 267
  20. 39
  21. 17
  22. 19
  23. 69
  24. 15
  25. 8
  26. 19
  27. 18
  28. 8
  29. 18
  30. 642
  31. 297
  32. 6
  33. 4
  34. 7
  35. 5
  36. 15
  37. 5
  38. 109
  39. 3
  40. 21

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