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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 920 · 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 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 149 (c) 140 (d) 158
  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) 51 (b) 17 (c) 54 (d) 153
  3. 3.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 474 (c) 604 (d) 594
  4. 4.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 162 (c) 154 (d) 153
  5. 5.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 352 (c) 420 (d) 421
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 8 (b) 18 (c) 19 (d) 20
  7. 7.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
  8. 8.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 438 (c) 370 (d) 448
  9. 9.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15
  10. 10.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 13 (b) 14 (c) 4 (d) 15
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  13. 13.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 6 (d) 7
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 3 (b) 2 (c) 1 (d) 4
  15. 15.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 182 (c) 164 (d) 173
  16. 16.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 22 (b) 40 (c) 32 (d) 31
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 4 (b) 6 (c) 3 (d) 5
  18. 18.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) 63 (c) 21 (d) 66
  19. 19.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 625 (b) 488 (c) 624 (d) 615
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 19 (b) 9 (c) 21 (d) 20
  21. 21.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  22. 22.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 5 (b) 6 (c) 4 (d) 3
  24. 24.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) 106 (c) 105 (d) 114
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 3 (b) 1 (c) 4 (d) 2
  26. 26.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  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) 42 (c) 39 (d) 13
  28. 28.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 357 (c) 310 (d) 348
  29. 29.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 198 (c) 66 (d) 69
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 19 (b) 17 (c) 8 (d) 18
  31. 31.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 65 (b) 74 (c) 56 (d) 66
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 20 (d) 9
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 19 (b) 7 (c) 18 (d) 17
  34. 34.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 21 (d) 19
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 14 (b) 15 (c) 13 (d) 3
  37. 37.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) 171 (b) 57 (c) 19 (d) 60
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 8 (b) 6 (c) 9 (d) 4
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 5 (b) 3 (c) 6 (d) 4
  40. 40.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3

Answer key

  1. 149
  2. 51
  3. 603
  4. 153
  5. 420
  6. 19
  7. 408
  8. 447
  9. 5
  10. 8
  11. 14
  12. 5
  13. 7
  14. 3
  15. 173
  16. 31
  17. 5
  18. 63
  19. 624
  20. 20
  21. 8
  22. 6
  23. 5
  24. 105
  25. 3
  26. 2
  27. 39
  28. 357
  29. 66
  30. 18
  31. 65
  32. 20
  33. 18
  34. 9
  35. 20
  36. 14
  37. 57
  38. 8
  39. 5
  40. 3

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