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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 315 · 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 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 142 (c) 151 (d) 152
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 19 (b) 17 (c) 8 (d) 18
  3. 3.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 331 (b) 330 (c) 292 (d) 321
  4. 4.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 610 (c) 600 (d) 609
  5. 5.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 358 (c) 310 (d) 357
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 2 (b) 4 (c) 3 (d) 5
  7. 7.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 420 (c) 523 (d) 513
  8. 8.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 2 (b) 3 (c) 4 (d) 1
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 18 (b) 7 (c) 17 (d) 19
  11. 11.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) 75 (b) 216 (c) 72 (d) 24
  12. 12.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 363 (c) 364 (d) 314
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 16 (b) 6 (c) 18 (d) 17
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 3 (b) 4 (c) 2 (d) 5
  15. 15.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 14 (b) 13 (c) 15 (d) 3
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 3 (b) 10 (c) 11 (d) 9
  18. 18.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) 62 (c) 61 (d) 70
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 7 (b) 18 (c) 17 (d) 19
  20. 20.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 188 (c) 187 (d) 178
  21. 21.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 57 (b) 66 (c) 48 (d) 58
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 3 (b) 4 (c) 5 (d) 2
  23. 23.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 9 (b) 18 (c) 20 (d) 19
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 3 (d) 2
  26. 26.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) 13 (b) 42 (c) 117 (d) 39
  27. 27.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 120 (c) 129 (d) 138
  28. 28.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  29. 29.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 337 (c) 296 (d) 336
  30. 30.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 418 (c) 417 (d) 350
  31. 31.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 464 (b) 579 (c) 588 (d) 589
  32. 32.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) 90 (c) 89 (d) 98
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 3 (b) 5 (c) 2 (d) 4
  34. 34.The numbers 3 to 11 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) 24 (c) 7 (d) 21
  35. 35.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) 162 (c) 18 (d) 54
  36. 36.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 97 (b) 98 (c) 106 (d) 88
  37. 37.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 157 (b) 148 (c) 166 (d) 158
  38. 38.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 139 (c) 140 (d) 130
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 15 (b) 17 (c) 16 (d) 7
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 10 (b) 8 (c) 3 (d) 9

Answer key

  1. 151
  2. 18
  3. 330
  4. 609
  5. 357
  6. 4
  7. 522
  8. 9
  9. 3
  10. 18
  11. 72
  12. 363
  13. 17
  14. 4
  15. 6
  16. 14
  17. 10
  18. 61
  19. 18
  20. 187
  21. 57
  22. 4
  23. 3
  24. 19
  25. 3
  26. 39
  27. 129
  28. 8
  29. 336
  30. 417
  31. 588
  32. 89
  33. 4
  34. 21
  35. 54
  36. 97
  37. 157
  38. 139
  39. 16
  40. 9

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