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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 676 · 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 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 247 (c) 246 (d) 236
  2. 2.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) 17 (c) 51 (d) 54
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 10 (b) 11 (c) 8 (d) 9
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 1 (b) 2 (c) 4 (d) 3
  5. 5.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) 30 (c) 10 (d) 33
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 14 (b) 15 (c) 13 (d) 3
  7. 7.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 460 (c) 450 (d) 459
  8. 8.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  9. 9.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) 21 (c) 66 (d) 189
  10. 10.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 11 (c) 9 (d) 10
  11. 11.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 523 (b) 522 (c) 513 (d) 420
  12. 12.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 8 (d) 9
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 4 (d) 5
  14. 14.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
  15. 15.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 17 (b) 5 (c) 15 (d) 16
  17. 17.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  18. 18.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) 63 (b) 60 (c) 20 (d) 180
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 6 (b) 17 (c) 15 (d) 16
  20. 20.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 17 (b) 6 (c) 16 (d) 18
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 18 (b) 20 (c) 9 (d) 19
  23. 23.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 114 (c) 96 (d) 105
  24. 24.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) 15 (c) 18 (d) 45
  25. 25.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  26. 26.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 477 (c) 487 (d) 486
  27. 27.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) 296 (c) 337 (d) 336
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 4 (b) 3 (c) 5 (d) 6
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 3 (b) 2 (c) 4 (d) 1
  30. 30.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 439 (b) 429 (c) 364 (d) 438
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 6 (b) 18 (c) 17 (d) 16
  33. 33.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 116 (c) 125 (d) 126
  34. 34.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 372 (c) 381 (d) 326
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 85? (a) 14 (b) 8 (c) 15 (d) 12
  36. 36.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 418 (c) 520 (d) 519
  37. 37.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 22 (b) 40 (c) 32 (d) 31
  38. 38.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 366 (c) 432 (d) 442
  39. 39.The numbers 3 to 11 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) 7 (c) 24 (d) 21
  40. 40.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 241 (b) 240 (c) 232 (d) 231

Answer key

  1. 246
  2. 51
  3. 10
  4. 3
  5. 30
  6. 14
  7. 459
  8. 5
  9. 63
  10. 9
  11. 522
  12. 8
  13. 5
  14. 6
  15. 7
  16. 16
  17. 6
  18. 60
  19. 16
  20. 7
  21. 17
  22. 19
  23. 105
  24. 15
  25. 9
  26. 486
  27. 336
  28. 5
  29. 3
  30. 438
  31. 2
  32. 17
  33. 125
  34. 381
  35. 14
  36. 519
  37. 31
  38. 441
  39. 21
  40. 240

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