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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 762 · 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.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 91 (b) 92 (c) 82 (d) 100
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 4 (b) 5 (c) 2 (d) 3
  3. 3.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) 33 (b) 30 (c) 10 (d) 90
  4. 4.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 4 (b) 14 (c) 15 (d) 16
  6. 6.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 49 (c) 50 (d) 58
  7. 7.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 631 (b) 630 (c) 492 (d) 621
  8. 8.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 442 (c) 546 (d) 556
  9. 9.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 87 (c) 88 (d) 96
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  11. 11.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 306 (c) 307 (d) 276
  12. 12.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 2 (d) 3
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 3 (d) 2
  14. 14.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) 11 (b) 36 (c) 99 (d) 33
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 15 (b) 16 (c) 5 (d) 17
  16. 16.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 217 (b) 324 (c) 216 (d) 207
  17. 17.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  18. 18.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 10 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 14 (d) 7
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 16 (b) 14 (c) 4 (d) 15
  21. 21.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) 27 (b) 81 (c) 30 (d) 9
  22. 22.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 43? (a) 3 (b) 5 (c) 4 (d) 2
  24. 24.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) 180 (b) 63 (c) 60 (d) 20
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 6 (b) 16 (c) 18 (d) 17
  26. 26.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  27. 27.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) 18 (b) 57 (c) 54 (d) 162
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 6 (b) 4 (c) 5 (d) 3
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 3 (b) 14 (c) 13 (d) 15
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 15 (b) 14 (c) 4 (d) 13
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 16 (b) 18 (c) 17 (d) 6
  32. 32.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) 66 (b) 21 (c) 189 (d) 63
  33. 33.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 56 (c) 66 (d) 65
  34. 34.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 16 (b) 17 (c) 18 (d) 6
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 1 (b) 2 (c) 3 (d) 4
  37. 37.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 277 (b) 267 (c) 276 (d) 256
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 19 (b) 18 (c) 7 (d) 17
  39. 39.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 147 (c) 138 (d) 156
  40. 40.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 150 (c) 140 (d) 149

Answer key

  1. 91
  2. 4
  3. 30
  4. 8
  5. 15
  6. 49
  7. 630
  8. 555
  9. 87
  10. 2
  11. 306
  12. 2
  13. 3
  14. 33
  15. 16
  16. 216
  17. 4
  18. 7
  19. 6
  20. 15
  21. 27
  22. 7
  23. 4
  24. 60
  25. 17
  26. 6
  27. 54
  28. 5
  29. 14
  30. 14
  31. 17
  32. 63
  33. 65
  34. 3
  35. 17
  36. 3
  37. 276
  38. 18
  39. 147
  40. 149

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