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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 970 · 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.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) 39 (c) 36 (d) 12
  2. 2.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) 135 (b) 15 (c) 48 (d) 45
  3. 3.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 158 (c) 157 (d) 148
  4. 4.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
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 46? (a) 4 (b) 13 (c) 12 (d) 11
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 19 (b) 8 (c) 20 (d) 18
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 18 (d) 19
  8. 8.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 98 (c) 107 (d) 108
  9. 9.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 286 (c) 262 (d) 276
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 90? (a) 19 (b) 9 (c) 18 (d) 20
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 5 (b) 8 (c) 6 (d) 7
  12. 12.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) 72 (b) 207 (c) 69 (d) 23
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 99? (a) 9 (b) 20 (c) 19 (d) 21
  14. 14.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 5 (d) 3
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 15 (b) 14 (c) 4 (d) 16
  16. 16.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) 90 (b) 33 (c) 10 (d) 30
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 9 (b) 19 (c) 21 (d) 20
  18. 18.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 71 (b) 62 (c) 80 (d) 72
  19. 19.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 550 (b) 549 (c) 540 (d) 438
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 3 (b) 4 (c) 1 (d) 2
  21. 21.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 81? (a) 19 (b) 8 (c) 17 (d) 18
  23. 23.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 295 (b) 294 (c) 268 (d) 285
  24. 24.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 58 (c) 67 (d) 76
  25. 25.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
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 15 (b) 13 (c) 3 (d) 14
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 11 (b) 3 (c) 9 (d) 10
  28. 28.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
  29. 29.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 501 (c) 492 (d) 502
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 9 (b) 21 (c) 20 (d) 19
  31. 31.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  32. 32.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
  33. 33.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 217 (c) 207 (d) 324
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 8 (b) 18 (c) 20 (d) 19
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 7 (b) 6 (c) 5 (d) 8
  36. 36.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  37. 37.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) 45 (d) 18
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 74? (a) 5 (b) 8 (c) 6 (d) 7
  39. 39.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 640 (c) 639 (d) 630
  40. 40.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) 11 (b) 33 (c) 99 (d) 36

Answer key

  1. 36
  2. 45
  3. 157
  4. 21
  5. 12
  6. 19
  7. 19
  8. 107
  9. 285
  10. 19
  11. 7
  12. 69
  13. 20
  14. 4
  15. 15
  16. 30
  17. 20
  18. 71
  19. 549
  20. 3
  21. 4
  22. 18
  23. 294
  24. 67
  25. 27
  26. 14
  27. 10
  28. 2
  29. 501
  30. 20
  31. 6
  32. 155
  33. 216
  34. 19
  35. 7
  36. 2
  37. 15
  38. 7
  39. 639
  40. 33

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