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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 243 · 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 56? (a) 15 (b) 5 (c) 17 (d) 16
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 19 (b) 17 (c) 18 (d) 8
  3. 3.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 71? (a) 18 (b) 17 (c) 16 (d) 7
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 6 (b) 15 (c) 16 (d) 17
  7. 7.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) 144 (b) 16 (c) 51 (d) 48
  8. 8.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 102 (c) 120 (d) 111
  9. 9.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) 60 (c) 63 (d) 20
  10. 10.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 6 (d) 4
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 18 (b) 19 (c) 7 (d) 17
  12. 12.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 164 (c) 173 (d) 182
  13. 13.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) 27 (d) 9
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 1 (b) 3 (c) 2 (d) 4
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 18 (b) 17 (c) 15 (d) 9
  16. 16.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) 153 (c) 17 (d) 51
  17. 17.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 62 (c) 61 (d) 52
  18. 18.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 18 (b) 19 (c) 8 (d) 20
  20. 20.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 507 (c) 416 (d) 517
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 19 (b) 17 (c) 8 (d) 18
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 17 (b) 6 (c) 16 (d) 18
  23. 23.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) 57 (c) 60 (d) 19
  24. 24.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
  25. 25.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) 69 (d) 23
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 14 (b) 16 (c) 4 (d) 15
  27. 27.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 129 (c) 130 (d) 120
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 20 (d) 19
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 16 (b) 18 (c) 6 (d) 17
  30. 30.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 149 (c) 158 (d) 140
  31. 31.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  32. 32.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 271 (b) 261 (c) 270 (d) 252
  33. 33.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  34. 34.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 179 (b) 180 (c) 188 (d) 170
  35. 35.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) 24 (c) 72 (d) 216
  36. 36.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 19 (b) 18 (c) 20 (d) 8
  38. 38.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 9 (b) 7 (c) 8 (d) 6
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 4 (b) 1 (c) 3 (d) 2

Answer key

  1. 16
  2. 18
  3. 4
  4. 17
  5. 4
  6. 16
  7. 48
  8. 111
  9. 60
  10. 5
  11. 18
  12. 173
  13. 27
  14. 3
  15. 17
  16. 51
  17. 61
  18. 6
  19. 19
  20. 516
  21. 18
  22. 17
  23. 57
  24. 30
  25. 69
  26. 15
  27. 129
  28. 20
  29. 17
  30. 149
  31. 9
  32. 270
  33. 3
  34. 179
  35. 72
  36. 2
  37. 19
  38. 7
  39. 8
  40. 3

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