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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 484 · 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.

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  1. 1.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) 222 (c) 225 (d) 216
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 3 (b) 2 (c) 5 (d) 4
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 17 (b) 15 (c) 5 (d) 16
  4. 4.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) 18 (b) 162 (c) 54 (d) 57
  5. 5.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
  6. 6.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 6 (b) 18 (c) 17 (d) 16
  8. 8.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) 27 (b) 72 (c) 8 (d) 24
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 14 (b) 5 (c) 16 (d) 15
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  11. 11.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 514 (b) 513 (c) 414 (d) 504
  12. 12.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 39 (c) 36 (d) 108
  13. 13.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 73 (c) 82 (d) 74
  14. 14.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 260 (b) 282 (c) 283 (d) 273
  15. 15.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
  16. 16.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) 90 (b) 33 (c) 30 (d) 10
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 9 (b) 10 (c) 8 (d) 7
  18. 18.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 19 (b) 18 (c) 9 (d) 20
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 16 (b) 17 (c) 5 (d) 15
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 13 (b) 15 (c) 3 (d) 14
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 10 (d) 2
  24. 24.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) 180 (b) 20 (c) 60 (d) 63
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 7 (b) 6 (c) 9 (d) 8
  27. 27.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 2 (b) 4 (c) 3 (d) 5
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  30. 30.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  31. 31.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 164 (c) 146 (d) 155
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 5 (b) 4 (c) 3 (d) 2
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 83? (a) 20 (b) 8 (c) 19 (d) 18
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 9 (b) 19 (c) 21 (d) 20
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 9 (b) 6 (c) 7 (d) 8
  36. 36.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  37. 37.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
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 4 (b) 3 (c) 2 (d) 5
  39. 39.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 494 (c) 633 (d) 634
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 6 (b) 17 (c) 18 (d) 16

Answer key

  1. 225
  2. 4
  3. 16
  4. 54
  5. 69
  6. 9
  7. 17
  8. 24
  9. 15
  10. 7
  11. 513
  12. 36
  13. 73
  14. 282
  15. 4
  16. 30
  17. 9
  18. 3
  19. 19
  20. 16
  21. 14
  22. 2
  23. 3
  24. 60
  25. 7
  26. 8
  27. 6
  28. 4
  29. 9
  30. 5
  31. 155
  32. 4
  33. 19
  34. 20
  35. 8
  36. 5
  37. 63
  38. 4
  39. 633
  40. 17

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