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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 71 · 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 5? (a) 6 (b) 4 (c) 5 (d) 10
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 3 (b) 4 (c) 5 (d) 6
  3. 3.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 499 (c) 404 (d) 498
  4. 4.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 90 (c) 80 (d) 89
  5. 5.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 588 (c) 598 (d) 470
  6. 6.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 59? (a) 5 (b) 7 (c) 6 (d) 4
  9. 9.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) 24 (b) 75 (c) 72 (d) 216
  10. 10.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  11. 11.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 325 (b) 324 (c) 315 (d) 288
  12. 12.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 234 (c) 243 (d) 351
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 73? (a) 16 (b) 18 (c) 17 (d) 7
  14. 14.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) 180 (c) 63 (d) 60
  15. 15.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
  16. 16.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) 117 (d) 13
  17. 17.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) 81 (d) 30
  18. 18.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  19. 19.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) 54 (b) 21 (c) 18 (d) 6
  20. 20.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 32 (c) 42 (d) 41
  21. 21.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 326 (c) 381 (d) 372
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 15 (b) 13 (c) 3 (d) 14
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 20 (b) 8 (c) 18 (d) 19
  24. 24.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 11 (b) 13 (c) 14 (d) 9
  26. 26.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 87 (c) 88 (d) 96
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 11 (d) 8
  28. 28.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 279 (c) 280 (d) 258
  29. 29.The numbers 14 to 22 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) 162 (c) 54 (d) 57
  30. 30.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 47 (c) 48 (d) 56
  31. 31.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 232 (d) 231
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 66? (a) 6 (b) 15 (c) 13 (d) 14
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 19 (b) 21 (c) 9 (d) 20
  34. 34.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 18 (b) 8 (c) 19 (d) 17
  36. 36.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 15 (b) 6 (c) 17 (d) 16
  38. 38.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 122 (c) 140 (d) 131
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 17 (b) 19 (c) 7 (d) 18
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 13 (b) 3 (c) 14 (d) 15

Answer key

  1. 5
  2. 5
  3. 498
  4. 89
  5. 597
  6. 6
  7. 4
  8. 6
  9. 72
  10. 4
  11. 324
  12. 243
  13. 17
  14. 60
  15. 8
  16. 39
  17. 27
  18. 7
  19. 18
  20. 41
  21. 381
  22. 14
  23. 19
  24. 5
  25. 13
  26. 87
  27. 9
  28. 279
  29. 54
  30. 47
  31. 231
  32. 14
  33. 20
  34. 7
  35. 18
  36. 2
  37. 16
  38. 131
  39. 18
  40. 14

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