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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 732 · 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 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 95 (c) 86 (d) 104
  2. 2.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) 11 (b) 99 (c) 33 (d) 36
  3. 3.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 9 (d) 11
  4. 4.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 17 (b) 16 (c) 18 (d) 6
  6. 6.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) 72 (d) 8
  7. 7.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 50 (c) 60 (d) 59
  8. 8.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 112 (c) 103 (d) 94
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 76? (a) 18 (b) 7 (c) 17 (d) 19
  10. 10.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) 23 (c) 207 (d) 72
  11. 11.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 11 (b) 12 (c) 3 (d) 13
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  14. 14.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) 13 (c) 42 (d) 39
  15. 15.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 113 (c) 114 (d) 104
  16. 16.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 60 (c) 42 (d) 51
  17. 17.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 4 (d) 6
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 4 (b) 5 (c) 2 (d) 3
  19. 19.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 27 (c) 81 (d) 30
  20. 20.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 4 (b) 6 (c) 7 (d) 5
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 14 (b) 3 (c) 13 (d) 15
  23. 23.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 450 (c) 378 (d) 459
  24. 24.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 46? (a) 3 (b) 4 (c) 2 (d) 5
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 19 (b) 17 (c) 18 (d) 8
  27. 27.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 288 (c) 264 (d) 289
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 73? (a) 18 (b) 16 (c) 7 (d) 17
  29. 29.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) 63 (c) 20 (d) 60
  30. 30.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 219 (c) 210 (d) 218
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 21 (b) 20 (c) 9 (d) 19
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 88? (a) 19 (b) 18 (c) 20 (d) 8
  33. 33.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 249 (c) 259 (d) 258
  34. 34.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 336 (c) 337 (d) 296
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 9 (b) 19 (c) 18 (d) 20
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 16 (b) 17 (c) 18 (d) 6
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 52? (a) 3 (b) 5 (c) 6 (d) 4
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 17 (b) 16 (c) 15 (d) 5
  39. 39.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 266 (c) 291 (d) 292
  40. 40.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) 189 (b) 63 (c) 66 (d) 21

Answer key

  1. 95
  2. 33
  3. 9
  4. 8
  5. 17
  6. 24
  7. 59
  8. 103
  9. 18
  10. 69
  11. 6
  12. 12
  13. 8
  14. 39
  15. 113
  16. 51
  17. 5
  18. 4
  19. 27
  20. 6
  21. 6
  22. 14
  23. 459
  24. 4
  25. 4
  26. 18
  27. 288
  28. 17
  29. 60
  30. 219
  31. 20
  32. 19
  33. 258
  34. 336
  35. 19
  36. 17
  37. 5
  38. 16
  39. 291
  40. 63

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