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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 418 · 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 two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 8 (d) 13
  2. 2.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 390 (c) 477 (d) 478
  3. 3.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 249 (c) 258 (d) 259
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 18 (b) 19 (c) 20 (d) 8
  6. 6.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  7. 7.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 56 (c) 47 (d) 38
  8. 8.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 622 (c) 612 (d) 621
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 4 (b) 5 (c) 3 (d) 2
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 66? (a) 7 (b) 5 (c) 4 (d) 6
  11. 11.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 18 (b) 8 (c) 19 (d) 17
  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) 18 (b) 162 (c) 54 (d) 57
  14. 14.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) 13 (c) 39 (d) 117
  15. 15.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 114 (c) 113 (d) 122
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 5 (b) 4 (c) 7 (d) 6
  17. 17.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
  18. 18.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) 51 (b) 54 (c) 17 (d) 153
  19. 19.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  20. 20.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
  21. 21.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 564 (c) 573 (d) 574
  22. 22.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  23. 23.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) 63 (c) 66 (d) 21
  24. 24.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) 63 (b) 24 (c) 7 (d) 21
  25. 25.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
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 16 (b) 6 (c) 17 (d) 15
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 8 (b) 19 (c) 20 (d) 18
  28. 28.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 6 (b) 5 (c) 3 (d) 4
  30. 30.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  31. 31.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) 90 (c) 10 (d) 30
  32. 32.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 117 (b) 108 (c) 118 (d) 126
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 19 (b) 20 (c) 8 (d) 18
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 8 (b) 18 (c) 19 (d) 20
  35. 35.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) 179 (c) 180 (d) 188
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 4 (b) 10 (c) 12 (d) 11
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 5 (b) 7 (c) 6 (d) 4
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 6 (b) 16 (c) 15 (d) 17
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 8 (b) 7 (c) 6 (d) 5
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 21 (d) 20

Answer key

  1. 7
  2. 477
  3. 258
  4. 4
  5. 19
  6. 2
  7. 47
  8. 621
  9. 4
  10. 6
  11. 5
  12. 18
  13. 54
  14. 39
  15. 113
  16. 6
  17. 33
  18. 51
  19. 3
  20. 48
  21. 573
  22. 9
  23. 63
  24. 21
  25. 42
  26. 16
  27. 19
  28. 4
  29. 5
  30. 8
  31. 30
  32. 117
  33. 19
  34. 19
  35. 179
  36. 11
  37. 6
  38. 16
  39. 7
  40. 20

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