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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 108 · 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 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 382 (c) 465 (d) 456
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 94? (a) 9 (b) 18 (c) 19 (d) 20
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 16 (b) 6 (c) 18 (d) 17
  4. 4.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 99 (b) 108 (c) 100 (d) 90
  5. 5.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  6. 6.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) 19 (c) 57 (d) 171
  7. 7.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 392 (b) 481 (c) 480 (d) 471
  8. 8.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  9. 9.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 547 (c) 537 (d) 546
  10. 10.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 291 (c) 266 (d) 282
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 5 (d) 4
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 8 (b) 19 (c) 18 (d) 17
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 16 (b) 18 (c) 6 (d) 17
  14. 14.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 4 (d) 6
  15. 15.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 3 (b) 14 (c) 13 (d) 15
  17. 17.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 463 (c) 462 (d) 380
  18. 18.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 3 (b) 6 (c) 5 (d) 4
  20. 20.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 232 (c) 240 (d) 241
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 9 (b) 20 (c) 19 (d) 21
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 5 (b) 7 (c) 6 (d) 8
  23. 23.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 396 (c) 487 (d) 486
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 20 (b) 18 (c) 9 (d) 19
  25. 25.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) 16 (b) 51 (c) 48 (d) 144
  26. 26.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 9 (d) 7
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 18 (d) 19
  28. 28.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
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 2 (b) 1 (c) 3 (d) 4
  30. 30.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) 234 (c) 351 (d) 243
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 16 (b) 5 (c) 14 (d) 15
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 13 (b) 15 (c) 3 (d) 14
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 6 (b) 8 (c) 7 (d) 5
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 6 (b) 4 (c) 3 (d) 5
  35. 35.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 558 (c) 568 (d) 450
  36. 36.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 270 (c) 279 (d) 258
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 15 (b) 16 (c) 5 (d) 17
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 19 (b) 17 (c) 7 (d) 18
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 15 (b) 16 (c) 5 (d) 14
  40. 40.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4

Answer key

  1. 465
  2. 19
  3. 17
  4. 99
  5. 2
  6. 57
  7. 480
  8. 5
  9. 546
  10. 291
  11. 5
  12. 18
  13. 17
  14. 5
  15. 9
  16. 14
  17. 462
  18. 8
  19. 5
  20. 240
  21. 20
  22. 7
  23. 486
  24. 19
  25. 48
  26. 8
  27. 18
  28. 21
  29. 3
  30. 243
  31. 15
  32. 14
  33. 7
  34. 5
  35. 567
  36. 279
  37. 16
  38. 18
  39. 15
  40. 4

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