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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 496 · 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 3 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 9 (d) 19
  2. 2.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) 11 (c) 36 (d) 33
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 84? (a) 20 (b) 18 (c) 19 (d) 8
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 21 (b) 9 (c) 20 (d) 19
  5. 5.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  6. 6.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 494 (b) 633 (c) 624 (d) 634
  7. 7.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  8. 8.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 133 (b) 142 (c) 134 (d) 124
  9. 9.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 96 (c) 105 (d) 114
  10. 10.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) 51 (b) 48 (c) 144 (d) 16
  11. 11.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) 63 (c) 180 (d) 60
  12. 12.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
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  14. 14.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 147 (c) 138 (d) 148
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 4 (b) 7 (c) 5 (d) 6
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 15 (b) 16 (c) 4 (d) 14
  17. 17.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) 63 (b) 189 (c) 21 (d) 66
  18. 18.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  19. 19.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) 6 (b) 18 (c) 54 (d) 21
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 1 (b) 2 (c) 3 (d) 4
  21. 21.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) 24 (b) 7 (c) 63 (d) 21
  22. 22.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 60 (c) 57 (d) 19
  23. 23.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  24. 24.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 38 (c) 48 (d) 47
  25. 25.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 85 (b) 86 (c) 76 (d) 94
  26. 26.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) 18 (b) 15 (c) 45 (d) 5
  27. 27.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 20 (b) 8 (c) 18 (d) 19
  29. 29.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 290 (c) 318 (d) 328
  30. 30.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 106 (c) 97 (d) 88
  31. 31.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 6 (b) 5 (c) 4 (d) 7
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 4 (b) 2 (c) 1 (d) 3
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 5 (b) 2 (c) 4 (d) 3
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 18 (b) 7 (c) 17 (d) 19
  36. 36.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
  37. 37.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
  38. 38.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 314 (b) 363 (c) 354 (d) 364
  39. 39.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) 9 (b) 81 (c) 27 (d) 30
  40. 40.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 603 (c) 474 (d) 604

Answer key

  1. 19
  2. 33
  3. 19
  4. 20
  5. 2
  6. 633
  7. 3
  8. 133
  9. 105
  10. 48
  11. 60
  12. 66
  13. 8
  14. 147
  15. 6
  16. 15
  17. 63
  18. 2
  19. 18
  20. 3
  21. 21
  22. 57
  23. 6
  24. 47
  25. 85
  26. 15
  27. 4
  28. 19
  29. 327
  30. 97
  31. 5
  32. 6
  33. 3
  34. 4
  35. 18
  36. 582
  37. 7
  38. 363
  39. 27
  40. 603

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