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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 85 · 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 2 written when you write all the numbers from 1 to 72? (a) 17 (b) 18 (c) 7 (d) 19
  2. 2.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) 435 (c) 436 (d) 362
  3. 3.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) 117 (b) 13 (c) 42 (d) 39
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4
  5. 5.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) 30 (b) 9 (c) 81 (d) 27
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 17 (b) 15 (c) 6 (d) 16
  7. 7.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 3 (d) 2
  8. 8.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) 126 (c) 42 (d) 14
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 4 (b) 5 (c) 6 (d) 7
  10. 10.The numbers 11 to 19 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) 48 (c) 15 (d) 135
  11. 11.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) 41 (c) 50 (d) 42
  12. 12.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 44 (c) 52 (d) 43
  13. 13.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 331 (b) 321 (c) 330 (d) 292
  14. 14.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 90 (c) 33 (d) 10
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 3 (b) 5 (c) 2 (d) 4
  16. 16.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 8 (b) 20 (c) 19 (d) 18
  18. 18.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 8 (d) 10
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 4 (b) 14 (c) 15 (d) 16
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 15 (b) 4 (c) 14 (d) 16
  21. 21.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 184 (c) 175 (d) 176
  22. 22.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 6 (d) 4
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 3 (b) 15 (c) 13 (d) 14
  24. 24.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 16 (b) 51 (c) 48 (d) 144
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 5 (b) 3 (c) 4 (d) 6
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 9 (d) 20
  27. 27.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  28. 28.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 77 (c) 86 (d) 68
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  30. 30.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 532 (b) 426 (c) 531 (d) 522
  31. 31.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) 207 (c) 72 (d) 69
  32. 32.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) 66 (b) 198 (c) 69 (d) 22
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 10 (b) 7 (c) 12 (d) 13
  34. 34.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) 36 (c) 12 (d) 108
  35. 35.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 207 (c) 198 (d) 208
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 5 (b) 16 (c) 15 (d) 17
  37. 37.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 13 (d) 6
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 14 (b) 4 (c) 16 (d) 15
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 7 (b) 6 (c) 5 (d) 8
  40. 40.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 24 (c) 7 (d) 63

Answer key

  1. 18
  2. 435
  3. 39
  4. 4
  5. 27
  6. 16
  7. 3
  8. 42
  9. 6
  10. 45
  11. 41
  12. 43
  13. 330
  14. 30
  15. 4
  16. 4
  17. 19
  18. 7
  19. 15
  20. 15
  21. 175
  22. 5
  23. 14
  24. 48
  25. 5
  26. 20
  27. 2
  28. 77
  29. 9
  30. 531
  31. 69
  32. 66
  33. 12
  34. 36
  35. 207
  36. 16
  37. 7
  38. 15
  39. 7
  40. 21

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