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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 624 · 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.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 45 (c) 14 (d) 42
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 92? (a) 18 (b) 9 (c) 20 (d) 19
  3. 3.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  5. 5.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 502 (b) 406 (c) 492 (d) 501
  6. 6.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 148 (c) 157 (d) 166
  7. 7.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 354 (c) 414 (d) 424
  8. 8.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 56 (c) 55 (d) 46
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 15 (b) 17 (c) 16 (d) 6
  10. 10.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 516 (c) 517 (d) 416
  11. 11.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) 106 (c) 97 (d) 98
  12. 12.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) 24 (b) 216 (c) 75 (d) 72
  13. 13.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) 198 (b) 22 (c) 69 (d) 66
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 15 (b) 13 (c) 14 (d) 3
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 14 (b) 16 (c) 15 (d) 4
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 18 (b) 20 (c) 9 (d) 19
  17. 17.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 9 (d) 11
  18. 18.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 640 (c) 630 (d) 639
  19. 19.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  20. 20.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 308 (c) 355 (d) 354
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 4 (b) 2 (c) 3 (d) 1
  22. 22.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
  23. 23.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 306 (c) 352 (d) 351
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 3 (b) 4 (c) 2 (d) 1
  25. 25.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) 45 (b) 18 (c) 5 (d) 15
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 19 (b) 18 (c) 17 (d) 8
  27. 27.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 1 (d) 2
  29. 29.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 9 (b) 21 (c) 20 (d) 19
  31. 31.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 51 (c) 16 (d) 48
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 3 (d) 4
  33. 33.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 68 (c) 67 (d) 58
  34. 34.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) 27 (d) 30
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 16 (b) 18 (c) 6 (d) 17
  36. 36.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) 483 (c) 474 (d) 394
  37. 37.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) 42 (c) 13 (d) 117
  38. 38.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  39. 39.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 594 (c) 604 (d) 603
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 8 (b) 19 (c) 20 (d) 18

Answer key

  1. 42
  2. 19
  3. 4
  4. 7
  5. 501
  6. 157
  7. 423
  8. 55
  9. 16
  10. 516
  11. 97
  12. 72
  13. 66
  14. 14
  15. 15
  16. 19
  17. 9
  18. 639
  19. 4
  20. 354
  21. 3
  22. 51
  23. 351
  24. 3
  25. 15
  26. 18
  27. 5
  28. 3
  29. 3
  30. 20
  31. 48
  32. 4
  33. 67
  34. 27
  35. 17
  36. 483
  37. 39
  38. 3
  39. 603
  40. 19

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