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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 94 · 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 92? (a) 18 (b) 19 (c) 9 (d) 20
  2. 2.The numbers 20 to 28 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) 75 (c) 216 (d) 72
  3. 3.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
  4. 4.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) 54 (b) 17 (c) 153 (d) 51
  5. 5.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  6. 6.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) 18 (c) 6 (d) 21
  7. 7.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 11 (b) 12 (c) 9 (d) 8
  9. 9.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) 63 (b) 180 (c) 20 (d) 60
  10. 10.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 2 (d) 3
  11. 11.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 259 (b) 249 (c) 244 (d) 258
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 15 (b) 16 (c) 17 (d) 5
  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) 57 (b) 54 (c) 162 (d) 18
  14. 14.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) 198 (b) 22 (c) 66 (d) 69
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 40? (a) 6 (b) 5 (c) 4 (d) 3
  16. 16.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 573 (c) 583 (d) 582
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 13 (b) 14 (c) 15 (d) 3
  18. 18.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 5 (b) 4 (c) 7 (d) 6
  20. 20.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 32 (c) 41 (d) 42
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 9 (b) 11 (c) 10 (d) 3
  22. 22.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 3 (b) 4 (c) 2 (d) 1
  24. 24.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 217 (c) 324 (d) 207
  25. 25.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 8 (d) 7
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 16 (b) 6 (c) 17 (d) 18
  27. 27.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 4 (b) 3 (c) 5 (d) 2
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 16 (b) 17 (c) 15 (d) 5
  31. 31.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 35 (c) 26 (d) 36
  32. 32.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 94? (a) 18 (b) 9 (c) 20 (d) 19
  34. 34.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 496 (b) 486 (c) 495 (d) 402
  35. 35.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 6 (b) 5 (c) 4 (d) 7
  37. 37.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) 72 (c) 207 (d) 23
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 55? (a) 4 (b) 5 (c) 6 (d) 3
  39. 39.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 7 (d) 9
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 14 (b) 16 (c) 15 (d) 5

Answer key

  1. 19
  2. 72
  3. 9
  4. 51
  5. 9
  6. 18
  7. 4
  8. 11
  9. 60
  10. 2
  11. 258
  12. 16
  13. 54
  14. 66
  15. 5
  16. 582
  17. 14
  18. 6
  19. 6
  20. 41
  21. 10
  22. 5
  23. 3
  24. 216
  25. 8
  26. 17
  27. 3
  28. 4
  29. 7
  30. 16
  31. 35
  32. 7
  33. 19
  34. 495
  35. 2
  36. 6
  37. 69
  38. 5
  39. 8
  40. 15

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