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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 581 · 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 96? (a) 21 (b) 19 (c) 9 (d) 20
  2. 2.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 174 (c) 166 (d) 165
  3. 3.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  4. 4.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 67 (b) 58 (c) 68 (d) 76
  5. 5.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) 57 (b) 54 (c) 18 (d) 162
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 7 (b) 8 (c) 6 (d) 9
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 6 (b) 5 (c) 7 (d) 4
  8. 8.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 4 (b) 3 (c) 5 (d) 2
  10. 10.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) 45 (b) 15 (c) 18 (d) 5
  11. 11.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) 207 (b) 72 (c) 23 (d) 69
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 17 (b) 6 (c) 16 (d) 18
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 19 (b) 20 (c) 8 (d) 18
  14. 14.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) 108 (d) 12
  15. 15.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) 63 (b) 180 (c) 20 (d) 60
  16. 16.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) 10 (b) 33 (c) 90 (d) 30
  17. 17.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 4 (b) 1 (c) 3 (d) 2
  19. 19.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 51 (c) 60 (d) 52
  20. 20.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  21. 21.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) 22 (c) 69 (d) 198
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 13 (b) 14 (c) 3 (d) 15
  23. 23.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 79 (b) 80 (c) 88 (d) 70
  24. 24.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) 60 (b) 19 (c) 57 (d) 171
  25. 25.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 368 (c) 445 (d) 435
  26. 26.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 504 (c) 505 (d) 495
  27. 27.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  28. 28.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 75 (c) 66 (d) 84
  29. 29.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) 99 (c) 33 (d) 36
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 14 (b) 13 (c) 3 (d) 15
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 16 (b) 15 (c) 17 (d) 6
  32. 32.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) 48 (b) 45 (c) 135 (d) 15
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 18 (b) 17 (c) 7 (d) 19
  34. 34.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 163 (c) 164 (d) 154
  35. 35.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 147 (b) 138 (c) 148 (d) 156
  36. 36.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 9 (b) 19 (c) 18 (d) 20
  38. 38.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 127 (c) 136 (d) 118
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 60? (a) 5 (b) 6 (c) 7 (d) 4
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 14 (b) 16 (c) 4 (d) 15

Answer key

  1. 20
  2. 165
  3. 4
  4. 67
  5. 54
  6. 8
  7. 6
  8. 7
  9. 4
  10. 15
  11. 69
  12. 17
  13. 19
  14. 36
  15. 60
  16. 30
  17. 2
  18. 3
  19. 51
  20. 2
  21. 66
  22. 14
  23. 79
  24. 57
  25. 444
  26. 504
  27. 3
  28. 75
  29. 33
  30. 14
  31. 16
  32. 45
  33. 18
  34. 163
  35. 147
  36. 8
  37. 19
  38. 127
  39. 6
  40. 15

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