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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 443 · 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 two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  2. 2.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 81 (c) 82 (d) 72
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 7 (b) 18 (c) 16 (d) 17
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 4 (b) 6 (c) 7 (d) 5
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 45? (a) 6 (b) 3 (c) 4 (d) 5
  6. 6.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 246 (c) 261 (d) 262
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 90? (a) 19 (b) 18 (c) 20 (d) 9
  8. 8.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) 492 (c) 502 (d) 501
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 15 (b) 14 (c) 16 (d) 4
  10. 10.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) 148 (d) 157
  11. 11.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 51 (c) 17 (d) 54
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 18 (b) 7 (c) 16 (d) 17
  13. 13.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
  14. 14.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 24 (c) 33 (d) 42
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 3 (b) 10 (c) 8 (d) 9
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 15 (b) 14 (c) 3 (d) 13
  17. 17.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 416 (c) 516 (d) 517
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 80? (a) 17 (b) 8 (c) 18 (d) 19
  19. 19.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 174 (c) 166 (d) 165
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 8 (b) 11 (c) 5 (d) 10
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 15 (b) 13 (c) 3 (d) 14
  22. 22.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 606 (c) 482 (d) 616
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 5 (b) 8 (c) 7 (d) 6
  24. 24.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 6 (b) 4 (c) 3 (d) 5
  26. 26.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
  27. 27.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  28. 28.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 123 (b) 132 (c) 124 (d) 114
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  30. 30.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 336 (c) 396 (d) 397
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  32. 32.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  33. 33.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) 486 (d) 396
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 16 (b) 15 (c) 4 (d) 14
  35. 35.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) 633 (c) 643 (d) 642
  36. 36.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  37. 37.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) 9 (b) 27 (c) 30 (d) 81
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 16 (b) 15 (c) 4 (d) 14
  39. 39.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 18 (b) 9 (c) 20 (d) 19

Answer key

  1. 3
  2. 81
  3. 17
  4. 6
  5. 5
  6. 261
  7. 19
  8. 501
  9. 15
  10. 157
  11. 51
  12. 17
  13. 7
  14. 33
  15. 9
  16. 14
  17. 516
  18. 18
  19. 165
  20. 10
  21. 14
  22. 615
  23. 7
  24. 3
  25. 5
  26. 36
  27. 5
  28. 123
  29. 6
  30. 396
  31. 2
  32. 2
  33. 486
  34. 15
  35. 642
  36. 9
  37. 27
  38. 15
  39. 4
  40. 19

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