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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 794 · 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 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 31 (b) 32 (c) 40 (d) 22
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 19 (d) 9
  4. 4.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 4 (b) 16 (c) 15 (d) 14
  6. 6.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  7. 7.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
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 19 (b) 18 (c) 7 (d) 17
  9. 9.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 541 (b) 531 (c) 540 (d) 432
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  11. 11.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) 60 (b) 20 (c) 180 (d) 63
  12. 12.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) 72 (b) 69 (c) 207 (d) 23
  13. 13.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 38 (c) 48 (d) 47
  14. 14.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 92 (c) 83 (d) 84
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 16 (b) 18 (c) 7 (d) 17
  16. 16.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) 376 (c) 456 (d) 457
  17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 71? (a) 17 (b) 18 (c) 7 (d) 16
  18. 18.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) 17 (c) 51 (d) 54
  19. 19.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) 27 (c) 8 (d) 72
  20. 20.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 496 (c) 495 (d) 402
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 18 (b) 17 (c) 16 (d) 7
  22. 22.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 107 (b) 116 (c) 98 (d) 108
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 19 (b) 8 (c) 18 (d) 17
  24. 24.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 1 (b) 4 (c) 3 (d) 2
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 78? (a) 7 (b) 17 (c) 18 (d) 19
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 20 (b) 8 (c) 19 (d) 18
  28. 28.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 16 (b) 18 (c) 6 (d) 17
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 14 (b) 3 (c) 13 (d) 12
  31. 31.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) 19 (c) 171 (d) 60
  32. 32.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 58 (c) 67 (d) 68
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 4 (b) 5 (c) 3 (d) 2
  34. 34.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 10 (d) 9
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 2 (b) 5 (c) 4 (d) 3
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 16 (b) 6 (c) 17 (d) 18
  37. 37.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 37 (c) 46 (d) 28
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 15 (d) 14
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 2 (b) 5 (c) 4 (d) 3
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 14 (b) 4 (c) 15 (d) 16

Answer key

  1. 31
  2. 9
  3. 19
  4. 7
  5. 15
  6. 4
  7. 30
  8. 18
  9. 540
  10. 2
  11. 60
  12. 69
  13. 47
  14. 83
  15. 17
  16. 456
  17. 17
  18. 51
  19. 24
  20. 495
  21. 17
  22. 107
  23. 18
  24. 7
  25. 3
  26. 18
  27. 19
  28. 2
  29. 17
  30. 13
  31. 57
  32. 67
  33. 4
  34. 9
  35. 4
  36. 17
  37. 37
  38. 15
  39. 4
  40. 15

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