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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 90 · 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.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) 45 (b) 15 (c) 18 (d) 5
  2. 2.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 615 (c) 482 (d) 616
  3. 3.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  4. 4.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 19 (d) 7
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 58? (a) 7 (b) 5 (c) 4 (d) 6
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 14 (b) 4 (c) 15 (d) 16
  8. 8.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 8 (d) 10
  9. 9.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
  10. 10.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 272 (c) 300 (d) 301
  11. 11.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 410 (c) 507 (d) 508
  12. 12.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 184 (c) 183 (d) 174
  13. 13.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 36 (c) 12 (d) 39
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 73? (a) 5 (b) 8 (c) 6 (d) 7
  15. 15.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 357 (c) 366 (d) 367
  16. 16.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 6 (b) 8 (c) 5 (d) 7
  18. 18.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) 21 (b) 63 (c) 24 (d) 7
  19. 19.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 613 (c) 612 (d) 603
  20. 20.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 501 (b) 511 (c) 510 (d) 412
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 2 (b) 4 (c) 1 (d) 3
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 82? (a) 17 (b) 8 (c) 19 (d) 18
  23. 23.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 4 (b) 6 (c) 5 (d) 7
  25. 25.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 18 (b) 17 (c) 19 (d) 7
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 89? (a) 18 (b) 8 (c) 19 (d) 20
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 17 (b) 18 (c) 16 (d) 6
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 13 (b) 15 (c) 14 (d) 3
  30. 30.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 149 (b) 158 (c) 140 (d) 150
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 57? (a) 13 (b) 5 (c) 14 (d) 15
  32. 32.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) 296 (d) 336
  33. 33.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 302 (b) 336 (c) 346 (d) 345
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 19 (b) 8 (c) 17 (d) 18
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  36. 36.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 56 (c) 46 (d) 55
  37. 37.The numbers 4 to 12 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) 27 (c) 24 (d) 8
  38. 38.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) 10 (b) 30 (c) 33 (d) 90
  39. 39.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 574 (c) 564 (d) 573
  40. 40.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) 637 (c) 636 (d) 627

Answer key

  1. 15
  2. 615
  3. 9
  4. 7
  5. 18
  6. 6
  7. 15
  8. 9
  9. 7
  10. 300
  11. 507
  12. 183
  13. 36
  14. 7
  15. 366
  16. 8
  17. 7
  18. 21
  19. 612
  20. 510
  21. 3
  22. 18
  23. 5
  24. 6
  25. 3
  26. 18
  27. 19
  28. 17
  29. 14
  30. 149
  31. 14
  32. 336
  33. 345
  34. 18
  35. 4
  36. 55
  37. 24
  38. 30
  39. 573
  40. 636

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