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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 239 · 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 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) 27 (b) 9 (c) 30 (d) 81
  2. 2.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 474 (c) 484 (d) 483
  3. 3.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 44 (c) 53 (d) 62
  4. 4.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 439 (c) 364 (d) 429
  5. 5.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 6 (b) 8 (c) 7 (d) 9
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  8. 8.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 10 (c) 30 (d) 33
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 8 (b) 7 (c) 6 (d) 5
  10. 10.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 565 (b) 448 (c) 564 (d) 555
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 8 (b) 7 (c) 5 (d) 6
  12. 12.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) 424 (c) 414 (d) 354
  13. 13.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) 153 (c) 51 (d) 54
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 57? (a) 5 (b) 15 (c) 13 (d) 14
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 20 (b) 9 (c) 21 (d) 19
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 4 (b) 2 (c) 3 (d) 5
  17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 3 (b) 5 (c) 4 (d) 6
  18. 18.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 5 (b) 3 (c) 4 (d) 2
  20. 20.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) 13 (c) 39 (d) 42
  21. 21.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) 24 (b) 72 (c) 8 (d) 27
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 7 (b) 4 (c) 6 (d) 5
  23. 23.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) 66 (d) 69
  24. 24.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) 21 (c) 66 (d) 63
  25. 25.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) 222 (c) 213 (d) 220
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 17 (b) 6 (c) 18 (d) 16
  27. 27.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 127 (b) 128 (c) 118 (d) 136
  28. 28.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) 7 (b) 63 (c) 24 (d) 21
  29. 29.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 8 (b) 9 (c) 6 (d) 5
  31. 31.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 324 (c) 334 (d) 333
  32. 32.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 397 (c) 336 (d) 396
  33. 33.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 79 (b) 88 (c) 70 (d) 80
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 2 (b) 1 (c) 4 (d) 3
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 14 (b) 15 (c) 4 (d) 16
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 8 (b) 12 (c) 11 (d) 9
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 7 (b) 17 (c) 16 (d) 18
  38. 38.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) 158 (c) 149 (d) 140
  39. 39.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 98 (c) 97 (d) 88
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 3 (d) 1

Answer key

  1. 27
  2. 483
  3. 53
  4. 438
  5. 7
  6. 8
  7. 2
  8. 30
  9. 7
  10. 564
  11. 7
  12. 423
  13. 51
  14. 14
  15. 20
  16. 4
  17. 5
  18. 7
  19. 4
  20. 39
  21. 24
  22. 6
  23. 66
  24. 63
  25. 222
  26. 17
  27. 127
  28. 21
  29. 3
  30. 8
  31. 333
  32. 396
  33. 79
  34. 3
  35. 15
  36. 11
  37. 17
  38. 149
  39. 97
  40. 3

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