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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 312 · 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 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 70 (c) 79 (d) 80
  2. 2.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) 36 (c) 12 (d) 108
  3. 3.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  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) 90 (c) 30 (d) 33
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 9 (b) 20 (c) 19 (d) 21
  6. 6.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 44 (c) 62 (d) 53
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  8. 8.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 436 (c) 435 (d) 362
  9. 9.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 122 (c) 114 (d) 113
  10. 10.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 337 (b) 296 (c) 327 (d) 336
  11. 11.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) 30 (d) 27
  12. 12.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 134 (c) 124 (d) 133
  13. 13.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) 8 (b) 72 (c) 27 (d) 24
  14. 14.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) 33 (b) 36 (c) 11 (d) 99
  15. 15.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 45 (b) 54 (c) 46 (d) 36
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 14 (b) 3 (c) 15 (d) 13
  17. 17.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
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 3 (b) 5 (c) 4 (d) 2
  19. 19.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 432 (c) 441 (d) 442
  20. 20.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 58? (a) 4 (b) 5 (c) 6 (d) 3
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 12 (b) 13 (c) 3 (d) 14
  23. 23.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 6 (d) 10
  24. 24.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 280 (c) 270 (d) 258
  25. 25.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 262 (c) 285 (d) 276
  26. 26.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  27. 27.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 16 (b) 17 (c) 6 (d) 15
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 6 (b) 15 (c) 17 (d) 16
  30. 30.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 256 (c) 276 (d) 277
  31. 31.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 613 (b) 480 (c) 612 (d) 603
  32. 32.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 165 (b) 174 (c) 166 (d) 156
  33. 33.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  34. 34.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  35. 35.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 358 (c) 348 (d) 357
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 6 (b) 5 (c) 8 (d) 7
  37. 37.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 16 (b) 14 (c) 15 (d) 4
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 18 (b) 16 (c) 17 (d) 7
  40. 40.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) 69 (b) 72 (c) 23 (d) 207

Answer key

  1. 79
  2. 36
  3. 8
  4. 30
  5. 20
  6. 53
  7. 6
  8. 435
  9. 113
  10. 336
  11. 27
  12. 133
  13. 24
  14. 33
  15. 45
  16. 14
  17. 3
  18. 4
  19. 441
  20. 4
  21. 5
  22. 13
  23. 5
  24. 279
  25. 285
  26. 4
  27. 7
  28. 16
  29. 16
  30. 276
  31. 612
  32. 165
  33. 9
  34. 2
  35. 357
  36. 7
  37. 2
  38. 15
  39. 17
  40. 69

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