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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 888 · 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 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 483 (c) 493 (d) 492
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 3 (b) 5 (c) 4 (d) 6
  3. 3.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 102 (c) 111 (d) 120
  4. 4.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) 14 (b) 126 (c) 42 (d) 45
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 1 (b) 2 (c) 4 (d) 3
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 7 (d) 18
  7. 7.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
  8. 8.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  9. 9.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) 60 (b) 171 (c) 57 (d) 19
  10. 10.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  11. 11.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  12. 12.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  13. 13.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 189 (c) 190 (d) 180
  14. 14.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 619 (c) 618 (d) 609
  15. 15.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 18 (b) 20 (c) 9 (d) 19
  17. 17.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 621 (c) 486 (d) 622
  18. 18.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  19. 19.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  20. 20.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 82 (c) 81 (d) 72
  21. 21.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 180 (c) 179 (d) 188
  22. 22.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 414 (c) 415 (d) 348
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 4 (b) 14 (c) 13 (d) 15
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 5 (b) 4 (c) 3 (d) 2
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 4 (b) 14 (c) 16 (d) 15
  26. 26.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) 24 (b) 21 (c) 7 (d) 63
  27. 27.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 487 (b) 486 (c) 396 (d) 477
  28. 28.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 165 (c) 166 (d) 156
  29. 29.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 15 (c) 45 (d) 48
  30. 30.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 297 (c) 276 (d) 307
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 3 (b) 1 (c) 2 (d) 4
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 18 (b) 17 (c) 7 (d) 16
  33. 33.The numbers 2 to 10 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) 54 (c) 6 (d) 18
  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) 51 (b) 153 (c) 17 (d) 54
  35. 35.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) 207 (b) 69 (c) 72 (d) 23
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 78? (a) 7 (b) 19 (c) 17 (d) 18
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 6 (b) 17 (c) 15 (d) 16
  38. 38.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) 20 (c) 180 (d) 60
  39. 39.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) 51 (b) 48 (c) 144 (d) 16
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 6 (b) 4 (c) 3 (d) 5

Answer key

  1. 492
  2. 5
  3. 111
  4. 42
  5. 3
  6. 18
  7. 396
  8. 7
  9. 57
  10. 5
  11. 4
  12. 5
  13. 189
  14. 618
  15. 8
  16. 19
  17. 621
  18. 8
  19. 2
  20. 81
  21. 179
  22. 414
  23. 14
  24. 4
  25. 15
  26. 21
  27. 486
  28. 165
  29. 45
  30. 306
  31. 3
  32. 17
  33. 18
  34. 51
  35. 69
  36. 18
  37. 16
  38. 60
  39. 48
  40. 5

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