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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 935 · 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 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 145 (b) 136 (c) 146 (d) 154
  2. 2.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) 72 (c) 216 (d) 24
  3. 3.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 90 (c) 108 (d) 99
  4. 4.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 68 (c) 78 (d) 77
  5. 5.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
  6. 6.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 255 (c) 248 (d) 265
  7. 7.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 83 (b) 74 (c) 84 (d) 92
  8. 8.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  9. 9.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
  10. 10.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) 18 (c) 162 (d) 54
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 17 (b) 16 (c) 15 (d) 5
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  13. 13.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) 33 (b) 99 (c) 36 (d) 11
  14. 14.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 186 (c) 195 (d) 202
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 13 (b) 14 (c) 3 (d) 15
  16. 16.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 2 (b) 5 (c) 3 (d) 4
  18. 18.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 218 (c) 220 (d) 210
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 3 (d) 4
  20. 20.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
  21. 21.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) 124 (c) 142 (d) 134
  22. 22.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) 100 (c) 82 (d) 92
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 4 (b) 5 (c) 3 (d) 2
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 6 (b) 7 (c) 5 (d) 8
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 9 (b) 21 (c) 20 (d) 19
  27. 27.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 241 (c) 232 (d) 240
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 2 (b) 3 (c) 4 (d) 1
  29. 29.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) 180 (c) 179 (d) 188
  30. 30.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 80 (c) 98 (d) 90
  31. 31.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) 13 (b) 42 (c) 117 (d) 39
  32. 32.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) 47 (c) 38 (d) 48
  33. 33.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 2 (b) 5 (c) 4 (d) 3
  35. 35.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  36. 36.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) 15 (d) 135
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 19 (b) 18 (c) 17 (d) 7
  38. 38.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 16 (b) 4 (c) 14 (d) 15
  40. 40.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) 23 (b) 207 (c) 72 (d) 69

Answer key

  1. 145
  2. 72
  3. 99
  4. 77
  5. 5
  6. 264
  7. 83
  8. 4
  9. 8
  10. 54
  11. 16
  12. 5
  13. 33
  14. 195
  15. 14
  16. 6
  17. 4
  18. 219
  19. 4
  20. 18
  21. 133
  22. 91
  23. 3
  24. 4
  25. 7
  26. 20
  27. 240
  28. 3
  29. 179
  30. 89
  31. 39
  32. 47
  33. 3
  34. 4
  35. 4
  36. 45
  37. 18
  38. 6
  39. 15
  40. 69

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