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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 101 · 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.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 15 (b) 17 (c) 6 (d) 16
  2. 2.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  3. 3.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 420 (c) 430 (d) 429
  4. 4.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) 60 (c) 180 (d) 20
  5. 5.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 490 (c) 627 (d) 628
  6. 6.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 113 (c) 104 (d) 122
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 15 (b) 5 (c) 16 (d) 14
  8. 8.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 423 (c) 424 (d) 414
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 4 (d) 5
  10. 10.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
  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) 24 (c) 72 (d) 216
  12. 12.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 457 (c) 456 (d) 376
  13. 13.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 543 (c) 434 (d) 544
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 2 (b) 3 (c) 4 (d) 5
  15. 15.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 634 (b) 494 (c) 624 (d) 633
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 5 (b) 4 (c) 6 (d) 7
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 10 (b) 9 (c) 11 (d) 8
  18. 18.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  19. 19.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 13 (b) 14 (c) 15 (d) 3
  21. 21.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) 21 (b) 189 (c) 63 (d) 66
  22. 22.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 103 (c) 104 (d) 112
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 20 (d) 8
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 64? (a) 7 (b) 6 (c) 5 (d) 4
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 4 (b) 3 (c) 6 (d) 5
  26. 26.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
  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) 98 (b) 80 (c) 90 (d) 89
  28. 28.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) 42 (b) 39 (c) 117 (d) 13
  29. 29.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) 8 (b) 24 (c) 72 (d) 27
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 65? (a) 6 (b) 12 (c) 10 (d) 13
  31. 31.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) 18 (c) 54 (d) 162
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 3 (b) 4 (c) 5 (d) 2
  33. 33.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 271 (b) 270 (c) 261 (d) 252
  34. 34.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) 153 (b) 51 (c) 17 (d) 54
  35. 35.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 600 (b) 609 (c) 478 (d) 610
  36. 36.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 72 (c) 207 (d) 23
  37. 37.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 135 (c) 136 (d) 126
  38. 38.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 306 (c) 282 (d) 316
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 6 (b) 17 (c) 16 (d) 18
  40. 40.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3

Answer key

  1. 16
  2. 4
  3. 429
  4. 60
  5. 627
  6. 113
  7. 15
  8. 423
  9. 4
  10. 3
  11. 72
  12. 456
  13. 543
  14. 4
  15. 633
  16. 6
  17. 10
  18. 2
  19. 9
  20. 14
  21. 63
  22. 103
  23. 19
  24. 6
  25. 5
  26. 8
  27. 89
  28. 39
  29. 24
  30. 12
  31. 54
  32. 4
  33. 270
  34. 51
  35. 609
  36. 69
  37. 135
  38. 315
  39. 17
  40. 2

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