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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 470 · 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 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 146 (c) 156 (d) 155
  2. 2.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) 48 (b) 135 (c) 45 (d) 15
  3. 3.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 8 (d) 9
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 18 (b) 17 (c) 16 (d) 6
  5. 5.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 438 (c) 550 (d) 549
  6. 6.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
  7. 7.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  8. 8.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 302 (c) 345 (d) 336
  9. 9.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 493 (c) 492 (d) 400
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 13 (b) 9 (c) 14 (d) 11
  11. 11.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  13. 13.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 198 (c) 208 (d) 210
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 20 (b) 19 (c) 9 (d) 21
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 5 (b) 7 (c) 8 (d) 6
  16. 16.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 45 (c) 42 (d) 14
  17. 17.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) 66 (b) 189 (c) 21 (d) 63
  18. 18.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 3 (b) 6 (c) 5 (d) 4
  21. 21.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) 19 (b) 60 (c) 57 (d) 171
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  23. 23.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  24. 24.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 6 (b) 4 (c) 5 (d) 3
  26. 26.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 514 (c) 414 (d) 513
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 94? (a) 9 (b) 20 (c) 21 (d) 19
  28. 28.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 469 (b) 384 (c) 459 (d) 468
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 2 (b) 4 (c) 5 (d) 3
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 18 (b) 20 (c) 19 (d) 8
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 5 (b) 6 (c) 4 (d) 3
  32. 32.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
  33. 33.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 379 (c) 378 (d) 369
  34. 34.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 14 (b) 16 (c) 15 (d) 5
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 57? (a) 15 (b) 5 (c) 14 (d) 13
  37. 37.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 603 (c) 480 (d) 613
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 1 (b) 3 (c) 4 (d) 2
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 14 (b) 15 (c) 13 (d) 3
  40. 40.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 81 (c) 82 (d) 72

Answer key

  1. 155
  2. 45
  3. 8
  4. 17
  5. 549
  6. 636
  7. 3
  8. 345
  9. 492
  10. 13
  11. 7
  12. 9
  13. 207
  14. 20
  15. 7
  16. 42
  17. 63
  18. 5
  19. 6
  20. 5
  21. 57
  22. 5
  23. 2
  24. 6
  25. 5
  26. 513
  27. 20
  28. 468
  29. 4
  30. 19
  31. 5
  32. 8
  33. 378
  34. 7
  35. 15
  36. 14
  37. 612
  38. 3
  39. 14
  40. 81

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