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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 755 · 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 5 written when you write all the numbers from 1 to 42? (a) 3 (b) 4 (c) 2 (d) 5
  2. 2.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) 126 (b) 42 (c) 14 (d) 45
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 4 (b) 14 (c) 16 (d) 15
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 18 (b) 19 (c) 20 (d) 8
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 9 (b) 20 (c) 21 (d) 19
  6. 6.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) 39 (b) 42 (c) 13 (d) 117
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 7 (b) 19 (c) 17 (d) 18
  8. 8.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 172 (c) 154 (d) 163
  9. 9.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 62 (c) 61 (d) 70
  10. 10.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 20 (c) 63 (d) 60
  11. 11.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) 9 (d) 30
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 7 (b) 9 (c) 8 (d) 6
  13. 13.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 483 (c) 484 (d) 394
  14. 14.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 307 (b) 276 (c) 306 (d) 297
  15. 15.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 17 (b) 16 (c) 18 (d) 6
  18. 18.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 556 (b) 442 (c) 555 (d) 546
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 11 (b) 9 (c) 12 (d) 7
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 4 (b) 5 (c) 6 (d) 3
  21. 21.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) 11 (c) 33 (d) 36
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  23. 23.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 82 (c) 81 (d) 90
  24. 24.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) 27 (c) 8 (d) 24
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 5 (b) 14 (c) 15 (d) 16
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 1 (b) 2 (c) 3 (d) 4
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 17 (b) 18 (c) 8 (d) 19
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 20 (b) 19 (c) 8 (d) 18
  29. 29.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) 135 (c) 15 (d) 45
  30. 30.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) 22 (b) 66 (c) 198 (d) 69
  31. 31.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  32. 32.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) 39 (b) 12 (c) 36 (d) 108
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 75? (a) 18 (b) 16 (c) 17 (d) 7
  34. 34.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 500 (c) 643 (d) 642
  35. 35.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) 24 (b) 63 (c) 21 (d) 7
  36. 36.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) 504 (c) 505 (d) 408
  37. 37.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  38. 38.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 116 (c) 115 (d) 124
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 6 (b) 5 (c) 8 (d) 7
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 1 (d) 4

Answer key

  1. 4
  2. 42
  3. 15
  4. 19
  5. 20
  6. 39
  7. 18
  8. 163
  9. 61
  10. 60
  11. 27
  12. 8
  13. 483
  14. 306
  15. 4
  16. 3
  17. 17
  18. 555
  19. 11
  20. 5
  21. 33
  22. 5
  23. 81
  24. 24
  25. 15
  26. 3
  27. 18
  28. 19
  29. 45
  30. 66
  31. 2
  32. 36
  33. 17
  34. 642
  35. 21
  36. 504
  37. 7
  38. 115
  39. 7
  40. 3

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