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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 827 · 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.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 5 (b) 15 (c) 16 (d) 17
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 15 (b) 13 (c) 3 (d) 14
  3. 3.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 600 (c) 472 (d) 601
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 3 (b) 11 (c) 10 (d) 12
  6. 6.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 3 (d) 2
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 7 (b) 5 (c) 6 (d) 4
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 85? (a) 8 (b) 19 (c) 20 (d) 18
  9. 9.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) 69 (c) 198 (d) 22
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 18 (b) 16 (c) 17 (d) 7
  11. 11.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 2 (b) 4 (c) 3 (d) 1
  13. 13.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
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 16 (b) 7 (c) 18 (d) 17
  15. 15.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 112 (c) 122 (d) 121
  16. 16.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 411 (c) 402 (d) 346
  17. 17.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 45 (b) 46 (c) 36 (d) 54
  18. 18.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) 13 (b) 39 (c) 42 (d) 117
  19. 19.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) 5 (b) 18 (c) 15 (d) 45
  20. 20.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) 54 (c) 17 (d) 51
  21. 21.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 114 (c) 123 (d) 124
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 20 (b) 19 (c) 9 (d) 18
  23. 23.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
  24. 24.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 114 (c) 113 (d) 122
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 5 (b) 3 (c) 4 (d) 2
  26. 26.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) 337 (c) 336 (d) 296
  27. 27.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 483 (c) 394 (d) 484
  28. 28.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 5 (b) 6 (c) 3 (d) 4
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 7 (b) 6 (c) 5 (d) 4
  31. 31.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) 225 (c) 222 (d) 216
  32. 32.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 625 (b) 488 (c) 624 (d) 615
  33. 33.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) 60 (c) 180 (d) 63
  34. 34.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) 279 (c) 264 (d) 288
  35. 35.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 19 (b) 21 (c) 9 (d) 20
  37. 37.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 580 (b) 458 (c) 579 (d) 570
  38. 38.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 339 (c) 298 (d) 340
  39. 39.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 253 (c) 243 (d) 252
  40. 40.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10

Answer key

  1. 16
  2. 14
  3. 600
  4. 7
  5. 11
  6. 3
  7. 6
  8. 19
  9. 66
  10. 17
  11. 2
  12. 3
  13. 69
  14. 17
  15. 121
  16. 411
  17. 45
  18. 39
  19. 15
  20. 51
  21. 123
  22. 19
  23. 9
  24. 113
  25. 4
  26. 336
  27. 483
  28. 4
  29. 5
  30. 6
  31. 225
  32. 624
  33. 60
  34. 288
  35. 8
  36. 20
  37. 579
  38. 339
  39. 252
  40. 9

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