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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 263 · 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.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  2. 2.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  3. 3.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) 24 (b) 8 (c) 72 (d) 27
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 16 (b) 4 (c) 15 (d) 14
  5. 5.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 505 (b) 495 (c) 504 (d) 408
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 17 (b) 16 (c) 7 (d) 18
  7. 7.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 20 (d) 9
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 4 (b) 6 (c) 3 (d) 5
  10. 10.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 499 (c) 404 (d) 498
  11. 11.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 105 (b) 114 (c) 106 (d) 96
  12. 12.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 60 (c) 68 (d) 59
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 20 (b) 21 (c) 9 (d) 19
  14. 14.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 48 (c) 30 (d) 39
  15. 15.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 4 (b) 3 (c) 2 (d) 5
  17. 17.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 99 (c) 36 (d) 11
  18. 18.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  19. 19.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) 45 (b) 14 (c) 42 (d) 126
  20. 20.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 154 (c) 172 (d) 163
  21. 21.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 20 (c) 60 (d) 63
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 72? (a) 7 (b) 6 (c) 5 (d) 8
  23. 23.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 322 (c) 312 (d) 321
  24. 24.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 496 (c) 402 (d) 495
  25. 25.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 61 (b) 70 (c) 52 (d) 62
  26. 26.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 549 (c) 559 (d) 558
  27. 27.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  28. 28.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 66 (c) 198 (d) 22
  29. 29.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 54 (c) 51 (d) 153
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 6 (b) 4 (c) 5 (d) 7
  31. 31.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
  32. 32.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  33. 33.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 582 (c) 583 (d) 460
  34. 34.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 113 (c) 114 (d) 122
  35. 35.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 342 (c) 352 (d) 306
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 9 (b) 18 (c) 20 (d) 19
  37. 37.The numbers 14 to 22 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) 57 (c) 54 (d) 162
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 6 (b) 16 (c) 18 (d) 17
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 5 (b) 3 (c) 4 (d) 2
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 65? (a) 6 (b) 16 (c) 18 (d) 17

Answer key

  1. 2
  2. 2
  3. 24
  4. 15
  5. 504
  6. 17
  7. 9
  8. 20
  9. 5
  10. 498
  11. 105
  12. 59
  13. 20
  14. 39
  15. 5
  16. 4
  17. 33
  18. 7
  19. 42
  20. 163
  21. 60
  22. 7
  23. 321
  24. 495
  25. 61
  26. 558
  27. 4
  28. 66
  29. 51
  30. 6
  31. 6
  32. 9
  33. 582
  34. 113
  35. 351
  36. 19
  37. 54
  38. 17
  39. 4
  40. 17

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