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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 158 · 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.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 619 (c) 618 (d) 609
  2. 2.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) 54 (b) 153 (c) 51 (d) 17
  3. 3.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) 180 (b) 20 (c) 60 (d) 63
  4. 4.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) 10 (b) 30 (c) 33 (d) 90
  5. 5.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 331 (c) 292 (d) 330
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 85? (a) 8 (b) 6 (c) 7 (d) 9
  7. 7.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 277 (b) 256 (c) 267 (d) 276
  8. 8.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 428 (c) 525 (d) 535
  9. 9.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) 36 (c) 39 (d) 12
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 20 (b) 18 (c) 8 (d) 19
  11. 11.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  12. 12.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 105 (c) 114 (d) 106
  13. 13.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
  14. 14.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 499 (b) 404 (c) 489 (d) 498
  15. 15.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 314 (b) 354 (c) 364 (d) 363
  16. 16.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) 189 (b) 66 (c) 21 (d) 63
  17. 17.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 302 (c) 345 (d) 346
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 14 (b) 16 (c) 15 (d) 4
  19. 19.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 70 (c) 62 (d) 61
  20. 20.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
  21. 21.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  22. 22.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 145 (b) 136 (c) 146 (d) 154
  23. 23.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
  24. 24.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) 216 (b) 24 (c) 75 (d) 72
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 3 (b) 13 (c) 14 (d) 15
  26. 26.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) 372 (c) 381 (d) 326
  27. 27.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) 117 (b) 13 (c) 42 (d) 39
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 65? (a) 4 (b) 7 (c) 5 (d) 6
  29. 29.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) 72 (b) 8 (c) 24 (d) 27
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 21 (b) 20 (c) 9 (d) 19
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 17 (b) 16 (c) 6 (d) 18
  32. 32.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  33. 33.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  34. 34.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 403 (b) 402 (c) 393 (d) 340
  35. 35.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
  36. 36.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  37. 37.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 12 (b) 11 (c) 9 (d) 10
  39. 39.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) 57 (b) 18 (c) 54 (d) 162
  40. 40.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8

Answer key

  1. 618
  2. 51
  3. 60
  4. 30
  5. 330
  6. 8
  7. 276
  8. 534
  9. 36
  10. 19
  11. 7
  12. 105
  13. 7
  14. 498
  15. 363
  16. 63
  17. 345
  18. 15
  19. 61
  20. 14
  21. 3
  22. 145
  23. 27
  24. 72
  25. 14
  26. 381
  27. 39
  28. 6
  29. 24
  30. 20
  31. 17
  32. 2
  33. 5
  34. 402
  35. 6
  36. 2
  37. 9
  38. 11
  39. 54
  40. 9

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