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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 156 · 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 6 written when you write all the numbers from 1 to 81? (a) 18 (b) 8 (c) 19 (d) 17
  2. 2.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) 21 (c) 6 (d) 54
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 1 (b) 2 (c) 3 (d) 4
  4. 4.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) 72 (b) 75 (c) 216 (d) 24
  5. 5.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 18 (b) 17 (c) 7 (d) 16
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 87? (a) 14 (b) 8 (c) 17 (d) 16
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 18 (b) 17 (c) 8 (d) 19
  10. 10.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  11. 11.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 532 (b) 522 (c) 426 (d) 531
  12. 12.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 7 (b) 17 (c) 18 (d) 19
  14. 14.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) 42 (b) 39 (c) 117 (d) 13
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 19 (b) 20 (c) 18 (d) 8
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 9 (b) 7 (c) 5 (d) 10
  17. 17.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 487 (c) 396 (d) 486
  18. 18.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 93? (a) 19 (b) 18 (c) 20 (d) 9
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 79? (a) 6 (b) 8 (c) 7 (d) 9
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 17 (b) 16 (c) 15 (d) 5
  22. 22.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 163 (b) 172 (c) 154 (d) 164
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 1 (d) 3
  24. 24.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 5 (b) 2 (c) 4 (d) 3
  26. 26.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) 21 (c) 24 (d) 63
  27. 27.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 57 (c) 58 (d) 48
  28. 28.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 89 (c) 90 (d) 98
  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) 45 (b) 135 (c) 48 (d) 15
  30. 30.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 339 (c) 348 (d) 304
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 4 (d) 3
  32. 32.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) 20 (b) 60 (c) 63 (d) 180
  33. 33.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 573 (c) 460 (d) 583
  34. 34.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 252 (c) 262 (d) 261
  35. 35.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 46 (c) 64 (d) 55
  36. 36.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) 36 (b) 11 (c) 33 (d) 99
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 2 (b) 4 (c) 5 (d) 3
  38. 38.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 489 (c) 499 (d) 404
  39. 39.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  40. 40.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3

Answer key

  1. 18
  2. 18
  3. 3
  4. 72
  5. 3
  6. 17
  7. 6
  8. 16
  9. 18
  10. 9
  11. 531
  12. 2
  13. 18
  14. 39
  15. 19
  16. 9
  17. 486
  18. 5
  19. 19
  20. 8
  21. 16
  22. 163
  23. 3
  24. 2
  25. 4
  26. 21
  27. 57
  28. 89
  29. 45
  30. 348
  31. 4
  32. 60
  33. 582
  34. 261
  35. 55
  36. 33
  37. 4
  38. 498
  39. 7
  40. 3

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