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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 614 · 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 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 604 (b) 594 (c) 603 (d) 474
  2. 2.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) 264 (c) 274 (d) 273
  3. 3.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 97 (c) 98 (d) 106
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 8 (b) 7 (c) 6 (d) 5
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 85? (a) 19 (b) 18 (c) 8 (d) 20
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  7. 7.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 21 (b) 20 (c) 19 (d) 9
  9. 9.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 2 (b) 3 (c) 4 (d) 5
  11. 11.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 171 (c) 172 (d) 180
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 6 (b) 14 (c) 15 (d) 16
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  15. 15.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 622 (b) 612 (c) 486 (d) 621
  16. 16.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 124 (c) 123 (d) 114
  17. 17.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) 162 (b) 57 (c) 54 (d) 18
  18. 18.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 223 (b) 213 (c) 220 (d) 222
  19. 19.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 208 (c) 205 (d) 204
  20. 20.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) 20 (c) 180 (d) 60
  21. 21.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 6 (b) 4 (c) 3 (d) 5
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 5 (b) 4 (c) 6 (d) 3
  24. 24.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) 117 (c) 42 (d) 13
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 65? (a) 6 (b) 17 (c) 16 (d) 18
  26. 26.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 496 (b) 495 (c) 486 (d) 402
  27. 27.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 98 (c) 89 (d) 90
  28. 28.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  29. 29.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 256 (c) 242 (d) 246
  30. 30.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 298 (c) 270 (d) 288
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 76? (a) 17 (b) 7 (c) 18 (d) 19
  32. 32.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  33. 33.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 344 (c) 399 (d) 409
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 19 (d) 17
  35. 35.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) 17 (c) 51 (d) 153
  36. 36.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 321 (c) 286 (d) 312
  37. 37.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
  38. 38.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 410 (c) 508 (d) 507
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 17 (b) 18 (c) 8 (d) 19
  40. 40.The numbers 1 to 9 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) 45 (c) 15 (d) 5

Answer key

  1. 603
  2. 273
  3. 97
  4. 7
  5. 19
  6. 9
  7. 5
  8. 20
  9. 3
  10. 4
  11. 171
  12. 9
  13. 15
  14. 7
  15. 621
  16. 123
  17. 54
  18. 222
  19. 204
  20. 60
  21. 5
  22. 5
  23. 5
  24. 39
  25. 17
  26. 495
  27. 89
  28. 8
  29. 255
  30. 297
  31. 18
  32. 3
  33. 408
  34. 18
  35. 51
  36. 321
  37. 357
  38. 507
  39. 18
  40. 15

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