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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 110 · 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 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 36 (c) 45 (d) 54
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 4 (b) 7 (c) 5 (d) 6
  3. 3.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 561 (c) 571 (d) 452
  4. 4.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) 66 (b) 198 (c) 22 (d) 69
  5. 5.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 535 (c) 428 (d) 534
  6. 6.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 17 (b) 18 (c) 8 (d) 19
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 8 (b) 18 (c) 19 (d) 17
  9. 9.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 40 (c) 31 (d) 22
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 9 (b) 11 (c) 4 (d) 10
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 9 (b) 11 (c) 10 (d) 8
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 5 (d) 3
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 3 (d) 1
  14. 14.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 460 (c) 573 (d) 583
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 62? (a) 17 (b) 16 (c) 6 (d) 15
  16. 16.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) 68 (c) 78 (d) 86
  17. 17.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  18. 18.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) 60 (b) 171 (c) 19 (d) 57
  19. 19.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) 63 (b) 189 (c) 21 (d) 66
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 1 (b) 4 (c) 3 (d) 2
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 18 (b) 20 (c) 19 (d) 8
  22. 22.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 149 (b) 158 (c) 150 (d) 140
  23. 23.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  24. 24.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 159 (b) 150 (c) 160 (d) 168
  25. 25.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) 36 (c) 33 (d) 99
  26. 26.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) 8 (c) 27 (d) 72
  27. 27.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 92 (c) 101 (d) 110
  28. 28.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) 108 (c) 36 (d) 39
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 82? (a) 18 (b) 19 (c) 17 (d) 8
  30. 30.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  31. 31.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 373 (b) 363 (c) 320 (d) 372
  32. 32.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) 14 (b) 42 (c) 126 (d) 45
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 1 (b) 4 (c) 2 (d) 3
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 9 (b) 21 (c) 20 (d) 19
  35. 35.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 208 (c) 210 (d) 198
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 2 (b) 1 (c) 3 (d) 4
  37. 37.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) 60 (c) 78 (d) 69
  38. 38.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 18 (c) 45 (d) 5
  39. 39.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 73 (b) 64 (c) 82 (d) 74
  40. 40.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 261 (c) 246 (d) 262

Answer key

  1. 45
  2. 6
  3. 570
  4. 66
  5. 534
  6. 7
  7. 18
  8. 18
  9. 31
  10. 10
  11. 10
  12. 4
  13. 3
  14. 582
  15. 16
  16. 77
  17. 3
  18. 57
  19. 63
  20. 3
  21. 19
  22. 149
  23. 9
  24. 159
  25. 33
  26. 24
  27. 101
  28. 36
  29. 18
  30. 8
  31. 372
  32. 42
  33. 3
  34. 20
  35. 207
  36. 3
  37. 69
  38. 15
  39. 73
  40. 261

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