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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 99 · 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 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 283 (c) 260 (d) 273
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 72? (a) 8 (b) 6 (c) 7 (d) 5
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 20 (b) 18 (c) 19 (d) 9
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 4 (d) 1
  5. 5.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) 21 (c) 24 (d) 7
  6. 6.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) 81 (b) 9 (c) 30 (d) 27
  7. 7.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10
  8. 8.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 315 (c) 325 (d) 288
  9. 9.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  10. 10.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 330 (c) 388 (d) 378
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 19 (b) 20 (c) 18 (d) 8
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 17 (b) 18 (c) 8 (d) 19
  13. 13.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 72 (c) 24 (d) 75
  14. 14.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 70 (c) 52 (d) 61
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 16 (b) 17 (c) 6 (d) 18
  16. 16.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) 33 (b) 10 (c) 30 (d) 90
  17. 17.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 349 (c) 348 (d) 339
  18. 18.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 43? (a) 2 (b) 3 (c) 4 (d) 5
  20. 20.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  21. 21.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 331 (b) 321 (c) 330 (d) 292
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 15 (b) 6 (c) 17 (d) 16
  23. 23.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) 57 (b) 171 (c) 60 (d) 19
  24. 24.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
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 4 (b) 2 (c) 1 (d) 3
  26. 26.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
  27. 27.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 86 (c) 77 (d) 78
  28. 28.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) 39 (c) 117 (d) 13
  29. 29.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 471 (c) 392 (d) 481
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 9 (b) 21 (c) 20 (d) 19
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 2 (b) 4 (c) 5 (d) 3
  32. 32.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) 54 (b) 17 (c) 51 (d) 153
  33. 33.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 5 (b) 3 (c) 2 (d) 4
  35. 35.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 7 (d) 9
  36. 36.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 643 (c) 500 (d) 642
  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) 180 (c) 63 (d) 60
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 4 (b) 2 (c) 3 (d) 1
  39. 39.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 496 (b) 627 (c) 636 (d) 637
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 2 (b) 3 (c) 5 (d) 4

Answer key

  1. 282
  2. 7
  3. 19
  4. 3
  5. 21
  6. 27
  7. 9
  8. 324
  9. 5
  10. 387
  11. 19
  12. 18
  13. 72
  14. 61
  15. 17
  16. 30
  17. 348
  18. 6
  19. 4
  20. 4
  21. 330
  22. 16
  23. 57
  24. 558
  25. 3
  26. 3
  27. 77
  28. 39
  29. 480
  30. 20
  31. 4
  32. 51
  33. 5
  34. 4
  35. 8
  36. 642
  37. 60
  38. 3
  39. 636
  40. 4

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