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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 328 · 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.

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  1. 1.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 204 (c) 205 (d) 195
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 17 (b) 15 (c) 16 (d) 5
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 2 (b) 1 (c) 3 (d) 4
  4. 4.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) 15 (c) 18 (d) 45
  5. 5.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
  6. 6.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 169 (c) 160 (d) 170
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 8 (b) 5 (c) 6 (d) 7
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 17 (b) 16 (c) 18 (d) 7
  9. 9.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) 81 (b) 30 (c) 9 (d) 27
  10. 10.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 18 (b) 7 (c) 17 (d) 16
  12. 12.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 387 (c) 397 (d) 396
  13. 13.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 630 (c) 621 (d) 631
  14. 14.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) 75 (b) 216 (c) 72 (d) 24
  15. 15.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 225 (b) 226 (c) 222 (d) 216
  16. 16.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) 60 (b) 20 (c) 180 (d) 63
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 93? (a) 19 (b) 9 (c) 18 (d) 20
  18. 18.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 6 (d) 15
  19. 19.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) 22 (c) 66 (d) 198
  20. 20.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 180 (c) 179 (d) 188
  21. 21.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 271 (c) 270 (d) 252
  22. 22.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) 99 (b) 36 (c) 11 (d) 33
  23. 23.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
  24. 24.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 580 (b) 570 (c) 458 (d) 579
  25. 25.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) 33 (c) 10 (d) 90
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 19 (b) 20 (c) 9 (d) 21
  27. 27.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
  28. 28.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) 7 (b) 63 (c) 24 (d) 21
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 7 (b) 4 (c) 6 (d) 5
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 6 (b) 4 (c) 7 (d) 3
  31. 31.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 87 (c) 96 (d) 78
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 1 (b) 4 (c) 3 (d) 2
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 19 (b) 21 (c) 9 (d) 20
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 9 (b) 19 (c) 18 (d) 20
  35. 35.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 18 (b) 20 (c) 8 (d) 19
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 20 (b) 18 (c) 8 (d) 19
  38. 38.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 113 (c) 104 (d) 122
  39. 39.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) 51 (d) 153
  40. 40.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 21 (c) 66 (d) 63

Answer key

  1. 204
  2. 16
  3. 3
  4. 15
  5. 8
  6. 169
  7. 7
  8. 17
  9. 27
  10. 9
  11. 17
  12. 396
  13. 630
  14. 72
  15. 225
  16. 60
  17. 19
  18. 5
  19. 66
  20. 179
  21. 270
  22. 33
  23. 2
  24. 579
  25. 30
  26. 20
  27. 39
  28. 21
  29. 6
  30. 6
  31. 87
  32. 3
  33. 20
  34. 19
  35. 4
  36. 19
  37. 19
  38. 113
  39. 51
  40. 63

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