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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 971 · 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 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) 9 (b) 81 (c) 27 (d) 30
  2. 2.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) 39 (b) 12 (c) 36 (d) 108
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 18 (b) 20 (c) 19 (d) 8
  4. 4.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  5. 5.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 270 (c) 297 (d) 288
  6. 6.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  7. 7.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 3 (d) 1
  9. 9.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 90 (c) 89 (d) 80
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 2 (b) 5 (c) 3 (d) 4
  11. 11.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 102 (c) 112 (d) 111
  12. 12.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 16 (b) 5 (c) 15 (d) 17
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 1 (b) 4 (c) 2 (d) 3
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 3 (b) 1 (c) 4 (d) 2
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 15 (b) 14 (c) 3 (d) 13
  17. 17.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  18. 18.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 340 (c) 393 (d) 403
  19. 19.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 6 (d) 15
  20. 20.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) 367 (d) 366
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 19 (b) 20 (c) 9 (d) 21
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 15 (b) 17 (c) 16 (d) 6
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 11 (b) 12 (c) 13 (d) 5
  24. 24.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  25. 25.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 23 (b) 72 (c) 69 (d) 207
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 6 (b) 9 (c) 7 (d) 8
  27. 27.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  28. 28.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  29. 29.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 213 (c) 214 (d) 204
  30. 30.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 319 (c) 284 (d) 309
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  32. 32.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) 5 (b) 18 (c) 15 (d) 45
  33. 33.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 487 (b) 486 (c) 477 (d) 396
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 6 (b) 5 (c) 4 (d) 3
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 17 (b) 7 (c) 18 (d) 19
  36. 36.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 354 (c) 308 (d) 355
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 3 (b) 15 (c) 14 (d) 13
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 92? (a) 9 (b) 18 (c) 19 (d) 20
  39. 39.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 93 (c) 94 (d) 102
  40. 40.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 540 (c) 531 (d) 541

Answer key

  1. 27
  2. 36
  3. 19
  4. 3
  5. 297
  6. 6
  7. 8
  8. 3
  9. 89
  10. 4
  11. 111
  12. 9
  13. 16
  14. 3
  15. 3
  16. 14
  17. 7
  18. 402
  19. 5
  20. 366
  21. 20
  22. 16
  23. 12
  24. 5
  25. 69
  26. 8
  27. 2
  28. 4
  29. 213
  30. 318
  31. 2
  32. 15
  33. 486
  34. 5
  35. 18
  36. 354
  37. 14
  38. 19
  39. 93
  40. 540

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