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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 781 · 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 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 156 (c) 147 (d) 148
  2. 2.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 65? (a) 7 (b) 6 (c) 4 (d) 5
  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) 24 (d) 216
  5. 5.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  6. 6.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 114 (c) 113 (d) 104
  7. 7.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 394 (c) 483 (d) 474
  8. 8.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) 30 (b) 27 (c) 81 (d) 9
  9. 9.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) 24 (c) 72 (d) 27
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 3 (b) 14 (c) 15 (d) 13
  11. 11.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  12. 12.The numbers 15 to 23 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) 60 (c) 171 (d) 19
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 66? (a) 6 (b) 14 (c) 15 (d) 13
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 7 (b) 6 (c) 9 (d) 10
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 14 (b) 4 (c) 15 (d) 16
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 4 (b) 15 (c) 14 (d) 16
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 1 (b) 3 (c) 4 (d) 2
  18. 18.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 254 (b) 273 (c) 274 (d) 264
  19. 19.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
  20. 20.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  21. 21.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  22. 22.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 384 (c) 393 (d) 394
  23. 23.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 16 (b) 17 (c) 18 (d) 7
  25. 25.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 169 (c) 160 (d) 170
  26. 26.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 505 (c) 504 (d) 495
  27. 27.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 571 (b) 570 (c) 561 (d) 452
  28. 28.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 13 (d) 6
  29. 29.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  30. 30.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 531 (c) 541 (d) 540
  31. 31.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 457 (c) 456 (d) 376
  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) 63 (b) 60 (c) 180 (d) 20
  33. 33.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  34. 34.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) 17 (b) 54 (c) 51 (d) 153
  35. 35.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 157 (c) 166 (d) 158
  36. 36.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 11 (d) 8
  37. 37.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 135 (c) 136 (d) 144
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 18 (d) 9
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 82? (a) 19 (b) 8 (c) 17 (d) 18
  40. 40.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 356 (b) 417 (c) 426 (d) 427

Answer key

  1. 147
  2. 8
  3. 6
  4. 72
  5. 2
  6. 113
  7. 483
  8. 27
  9. 24
  10. 14
  11. 9
  12. 57
  13. 14
  14. 9
  15. 15
  16. 15
  17. 3
  18. 273
  19. 33
  20. 6
  21. 7
  22. 393
  23. 5
  24. 17
  25. 169
  26. 504
  27. 570
  28. 7
  29. 2
  30. 540
  31. 456
  32. 60
  33. 4
  34. 51
  35. 157
  36. 9
  37. 135
  38. 19
  39. 18
  40. 426

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