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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 374 · 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 two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  2. 2.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 225 (c) 222 (d) 216
  3. 3.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  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) 364 (b) 429 (c) 439 (d) 438
  5. 5.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  6. 6.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
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 15 (b) 17 (c) 5 (d) 16
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 4 (b) 3 (c) 5 (d) 6
  10. 10.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) 66 (d) 63
  11. 11.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 643 (b) 500 (c) 633 (d) 642
  12. 12.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 32 (c) 41 (d) 50
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
  14. 14.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 254 (c) 273 (d) 274
  15. 15.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 537 (b) 547 (c) 436 (d) 546
  16. 16.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) 45 (c) 15 (d) 48
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 7 (b) 19 (c) 18 (d) 17
  18. 18.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 625 (c) 615 (d) 488
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 15 (b) 13 (c) 3 (d) 14
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  21. 21.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
  22. 22.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 77 (b) 78 (c) 86 (d) 68
  23. 23.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 17 (b) 19 (c) 18 (d) 8
  25. 25.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
  26. 26.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  27. 27.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) 10 (b) 33 (c) 90 (d) 30
  28. 28.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 33 (c) 24 (d) 34
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 5 (b) 4 (c) 3 (d) 6
  30. 30.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 229 (b) 219 (c) 228 (d) 224
  31. 31.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  32. 32.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 571 (c) 452 (d) 570
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 87? (a) 6 (b) 9 (c) 7 (d) 8
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 7 (b) 8 (c) 6 (d) 5
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 9 (d) 20
  36. 36.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 567 (c) 577 (d) 456
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 5 (b) 2 (c) 4 (d) 3
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 16 (b) 15 (c) 17 (d) 6
  39. 39.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 36 (c) 33 (d) 11
  40. 40.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 62 (c) 52 (d) 61

Answer key

  1. 5
  2. 225
  3. 2
  4. 438
  5. 7
  6. 18
  7. 16
  8. 8
  9. 5
  10. 63
  11. 642
  12. 41
  13. 8
  14. 273
  15. 546
  16. 45
  17. 18
  18. 624
  19. 14
  20. 3
  21. 66
  22. 77
  23. 5
  24. 18
  25. 24
  26. 2
  27. 30
  28. 33
  29. 5
  30. 228
  31. 4
  32. 570
  33. 8
  34. 7
  35. 20
  36. 576
  37. 4
  38. 16
  39. 33
  40. 61

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