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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 770 · 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 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 157 (b) 148 (c) 166 (d) 158
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 21 (d) 20
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 4 (b) 5 (c) 6 (d) 7
  4. 4.The numbers 2 to 10 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) 6 (c) 21 (d) 18
  5. 5.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 13 (b) 3 (c) 14 (d) 12
  7. 7.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  8. 8.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 62 (c) 53 (d) 54
  9. 9.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
  10. 10.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 85 (b) 94 (c) 86 (d) 76
  11. 11.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) 30 (b) 10 (c) 33 (d) 90
  12. 12.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 243 (c) 234 (d) 351
  13. 13.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 140 (c) 149 (d) 158
  14. 14.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 444 (c) 559 (d) 549
  15. 15.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 60 (c) 51 (d) 52
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 3 (b) 1 (c) 4 (d) 2
  17. 17.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
  18. 18.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) 155 (c) 146 (d) 164
  19. 19.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) 15 (b) 135 (c) 48 (d) 45
  20. 20.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 615 (c) 625 (d) 488
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 1 (b) 4 (c) 2 (d) 3
  22. 22.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 289 (b) 264 (c) 279 (d) 288
  23. 23.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 139 (b) 140 (c) 148 (d) 130
  24. 24.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 438 (c) 448 (d) 447
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 96? (a) 14 (b) 16 (c) 17 (d) 9
  26. 26.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 332 (b) 390 (c) 381 (d) 391
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 17 (b) 15 (c) 5 (d) 16
  28. 28.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 2 (b) 4 (c) 5 (d) 3
  30. 30.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
  31. 31.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 144 (c) 16 (d) 48
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 3 (b) 5 (c) 2 (d) 4
  33. 33.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) 218 (d) 210
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 2 (b) 3 (c) 5 (d) 4
  35. 35.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) 57 (d) 19
  36. 36.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
  37. 37.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
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 13 (b) 3 (c) 14 (d) 15
  39. 39.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) 42 (b) 13 (c) 39 (d) 117
  40. 40.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 609 (c) 600 (d) 478

Answer key

  1. 157
  2. 20
  3. 6
  4. 18
  5. 3
  6. 13
  7. 7
  8. 53
  9. 24
  10. 85
  11. 30
  12. 243
  13. 149
  14. 558
  15. 51
  16. 3
  17. 3
  18. 155
  19. 45
  20. 624
  21. 3
  22. 288
  23. 139
  24. 447
  25. 16
  26. 390
  27. 16
  28. 4
  29. 4
  30. 4
  31. 48
  32. 4
  33. 219
  34. 4
  35. 57
  36. 7
  37. 60
  38. 14
  39. 39
  40. 609

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