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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 400 · 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 8 written when you write all the numbers from 1 to 75? (a) 8 (b) 6 (c) 7 (d) 5
  2. 2.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) 118 (c) 110 (d) 100
  3. 3.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) 8 (c) 24 (d) 72
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 13 (b) 15 (c) 8 (d) 16
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 19 (d) 20
  6. 6.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 429 (c) 438 (d) 439
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 17 (b) 18 (c) 19 (d) 7
  8. 8.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  9. 9.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
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 7 (b) 8 (c) 9 (d) 6
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 17 (b) 16 (c) 18 (d) 6
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 19 (b) 8 (c) 17 (d) 18
  13. 13.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) 108 (d) 36
  14. 14.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 468 (c) 478 (d) 390
  15. 15.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 414 (c) 514 (d) 504
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3
  17. 17.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  18. 18.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  19. 19.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) 51 (b) 48 (c) 16 (d) 144
  20. 20.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) 27 (c) 9 (d) 81
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 31? (a) 1 (b) 3 (c) 4 (d) 2
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 20 (b) 8 (c) 19 (d) 18
  23. 23.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 3 (b) 4 (c) 2 (d) 5
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 3 (b) 1 (c) 4 (d) 2
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 4 (b) 16 (c) 14 (d) 15
  27. 27.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 82 (c) 64 (d) 73
  28. 28.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 43 (b) 34 (c) 52 (d) 44
  29. 29.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 139 (c) 148 (d) 140
  30. 30.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 10 (b) 11 (c) 12 (d) 9
  32. 32.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) 5 (b) 15 (c) 18 (d) 45
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 4 (b) 14 (c) 13 (d) 15
  34. 34.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 66 (c) 189 (d) 63
  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) 7 (b) 24 (c) 21 (d) 63
  36. 36.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  37. 37.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 4 (b) 7 (c) 5 (d) 6
  39. 39.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 110 (c) 101 (d) 102
  40. 40.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 128 (c) 146 (d) 137

Answer key

  1. 7
  2. 109
  3. 24
  4. 15
  5. 19
  6. 438
  7. 18
  8. 9
  9. 45
  10. 8
  11. 17
  12. 18
  13. 36
  14. 477
  15. 513
  16. 3
  17. 7
  18. 5
  19. 48
  20. 27
  21. 3
  22. 19
  23. 2
  24. 4
  25. 3
  26. 15
  27. 73
  28. 43
  29. 139
  30. 6
  31. 11
  32. 15
  33. 14
  34. 63
  35. 21
  36. 5
  37. 4
  38. 6
  39. 101
  40. 137

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