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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 641 · 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 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) 171 (c) 19 (d) 57
  2. 2.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  3. 3.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) 18 (b) 45 (c) 5 (d) 15
  4. 4.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) 12 (b) 36 (c) 108 (d) 39
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 3 (b) 5 (c) 4 (d) 2
  6. 6.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 135 (b) 144 (c) 126 (d) 136
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 16 (b) 17 (c) 6 (d) 18
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 7 (b) 4 (c) 6 (d) 5
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 7 (b) 8 (c) 3 (d) 9
  10. 10.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 598 (b) 470 (c) 597 (d) 588
  11. 11.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 7 (b) 18 (c) 16 (d) 17
  13. 13.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 92 (c) 83 (d) 84
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 20 (d) 18
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 8 (b) 19 (c) 17 (d) 18
  16. 16.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 42 (c) 50 (d) 41
  17. 17.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  18. 18.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  19. 19.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 18 (b) 17 (c) 6 (d) 16
  21. 21.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  22. 22.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
  23. 23.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
  24. 24.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 89 (c) 98 (d) 80
  25. 25.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) 326 (c) 381 (d) 372
  26. 26.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 198 (c) 180 (d) 189
  27. 27.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 3 (d) 10
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 17 (d) 16
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 6 (b) 8 (c) 7 (d) 9
  30. 30.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 98 (c) 88 (d) 97
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 17 (b) 18 (c) 8 (d) 19
  32. 32.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 396 (c) 487 (d) 477
  33. 33.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 87 (c) 88 (d) 96
  34. 34.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 519 (b) 529 (c) 528 (d) 424
  35. 35.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 619 (c) 609 (d) 618
  36. 36.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 254 (c) 274 (d) 273
  37. 37.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 374 (c) 453 (d) 444
  38. 38.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 514 (b) 513 (c) 414 (d) 504
  39. 39.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 286 (c) 285 (d) 262
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 3 (b) 5 (c) 2 (d) 4

Answer key

  1. 57
  2. 9
  3. 15
  4. 36
  5. 4
  6. 135
  7. 17
  8. 6
  9. 8
  10. 597
  11. 9
  12. 17
  13. 83
  14. 19
  15. 18
  16. 41
  17. 8
  18. 2
  19. 2
  20. 17
  21. 5
  22. 6
  23. 4
  24. 89
  25. 381
  26. 189
  27. 4
  28. 17
  29. 8
  30. 97
  31. 18
  32. 486
  33. 87
  34. 528
  35. 618
  36. 273
  37. 453
  38. 513
  39. 285
  40. 4

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