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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 458 · 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 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) 45 (b) 15 (c) 135 (d) 48
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 17 (b) 18 (c) 7 (d) 19
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 5 (b) 6 (c) 4 (d) 7
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
  5. 5.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) 45 (b) 14 (c) 126 (d) 42
  6. 6.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 336 (c) 327 (d) 337
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  8. 8.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  9. 9.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 19 (b) 18 (c) 20 (d) 8
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 7 (b) 17 (c) 19 (d) 18
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 4 (b) 5 (c) 3 (d) 6
  13. 13.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 619 (b) 618 (c) 484 (d) 609
  14. 14.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 8 (b) 18 (c) 20 (d) 19
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 16 (b) 18 (c) 7 (d) 17
  17. 17.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  18. 18.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) 54 (b) 57 (c) 162 (d) 18
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 7 (b) 6 (c) 4 (d) 5
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 19 (b) 18 (c) 20 (d) 8
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  22. 22.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) 57 (b) 60 (c) 171 (d) 19
  23. 23.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) 20 (b) 63 (c) 180 (d) 60
  24. 24.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 18 (b) 6 (c) 16 (d) 17
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 19 (b) 17 (c) 8 (d) 18
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 17 (b) 18 (c) 6 (d) 16
  28. 28.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) 66 (b) 189 (c) 21 (d) 63
  29. 29.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 505 (c) 408 (d) 504
  30. 30.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 18 (d) 17
  32. 32.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 382 (c) 326 (d) 381
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 4 (b) 8 (c) 5 (d) 7
  34. 34.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 69 (c) 78 (d) 60
  35. 35.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  36. 36.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) 39 (c) 42 (d) 13
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 6 (b) 17 (c) 16 (d) 15
  38. 38.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) 72 (c) 69 (d) 23
  39. 39.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 57 (c) 48 (d) 58
  40. 40.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) 72 (c) 81 (d) 82

Answer key

  1. 45
  2. 18
  3. 6
  4. 2
  5. 42
  6. 336
  7. 4
  8. 9
  9. 3
  10. 19
  11. 18
  12. 5
  13. 618
  14. 5
  15. 19
  16. 17
  17. 8
  18. 54
  19. 6
  20. 19
  21. 7
  22. 57
  23. 60
  24. 8
  25. 17
  26. 18
  27. 17
  28. 63
  29. 504
  30. 3
  31. 18
  32. 381
  33. 7
  34. 69
  35. 9
  36. 39
  37. 16
  38. 69
  39. 57
  40. 81

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