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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 486 · 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 times is the digit 6 written when you write all the numbers from 1 to 95? (a) 20 (b) 18 (c) 9 (d) 19
  2. 2.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
  3. 3.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 9 (b) 10 (c) 11 (d) 8
  5. 5.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 117 (c) 39 (d) 13
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  7. 7.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) 69 (b) 207 (c) 23 (d) 72
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 5 (b) 6 (c) 3 (d) 4
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 2 (b) 3 (c) 1 (d) 4
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 7 (b) 4 (c) 8 (d) 5
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 16 (b) 4 (c) 15 (d) 14
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 18 (b) 19 (c) 9 (d) 20
  13. 13.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) 162 (b) 54 (c) 18 (d) 57
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 14 (b) 15 (c) 13 (d) 3
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 15 (b) 5 (c) 17 (d) 16
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 17 (b) 16 (c) 6 (d) 15
  17. 17.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10
  18. 18.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 537 (b) 538 (c) 528 (d) 430
  19. 19.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 210 (c) 207 (d) 198
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 3 (b) 5 (c) 2 (d) 4
  21. 21.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 1 (d) 18
  22. 22.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 262 (c) 246 (d) 261
  23. 23.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 119 (b) 120 (c) 128 (d) 110
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 18 (b) 19 (c) 20 (d) 8
  25. 25.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 6 (c) 21 (d) 18
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 16 (b) 6 (c) 15 (d) 17
  27. 27.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 3 (d) 4
  29. 29.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  30. 30.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) 11 (c) 36 (d) 99
  31. 31.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) 20 (b) 180 (c) 60 (d) 63
  32. 32.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 21 (b) 20 (c) 9 (d) 19
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 2 (b) 3 (c) 5 (d) 4
  35. 35.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 362 (c) 436 (d) 435
  36. 36.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 19 (b) 20 (c) 18 (d) 8
  38. 38.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 613 (b) 480 (c) 603 (d) 612
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 8 (b) 18 (c) 19 (d) 20
  40. 40.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

Answer key

  1. 19
  2. 5
  3. 4
  4. 10
  5. 39
  6. 2
  7. 69
  8. 5
  9. 3
  10. 7
  11. 15
  12. 19
  13. 54
  14. 14
  15. 16
  16. 16
  17. 9
  18. 537
  19. 207
  20. 4
  21. 2
  22. 261
  23. 119
  24. 19
  25. 18
  26. 16
  27. 9
  28. 3
  29. 7
  30. 33
  31. 60
  32. 3
  33. 20
  34. 4
  35. 435
  36. 6
  37. 19
  38. 612
  39. 19
  40. 498

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