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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 997 · 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 7 written when you write all the numbers from 1 to 81? (a) 17 (b) 19 (c) 18 (d) 8
  2. 2.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 4 (d) 3
  3. 3.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) 15 (b) 135 (c) 48 (d) 45
  4. 4.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 288 (c) 270 (d) 298
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 13 (b) 10 (c) 7 (d) 12
  6. 6.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
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 89? (a) 20 (b) 19 (c) 18 (d) 8
  8. 8.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 37 (c) 46 (d) 28
  9. 9.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 520 (c) 519 (d) 510
  10. 10.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) 90 (d) 10
  11. 11.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) 54 (b) 162 (c) 57 (d) 18
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 17 (b) 16 (c) 6 (d) 18
  13. 13.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 225 (b) 235 (c) 234 (d) 228
  14. 14.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 134 (c) 133 (d) 142
  15. 15.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 21 (d) 20
  17. 17.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) 7 (b) 24 (c) 21 (d) 63
  18. 18.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 146 (c) 164 (d) 155
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 3 (b) 14 (c) 13 (d) 15
  20. 20.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 13 (b) 14 (c) 15 (d) 3
  22. 22.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  23. 23.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 19 (d) 20
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 94? (a) 9 (b) 21 (c) 19 (d) 20
  26. 26.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 163 (c) 154 (d) 172
  27. 27.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) 14 (c) 42 (d) 126
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 66? (a) 7 (b) 4 (c) 5 (d) 6
  29. 29.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  30. 30.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 152 (c) 134 (d) 143
  31. 31.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
  32. 32.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 95 (c) 96 (d) 104
  33. 33.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) 60 (c) 57 (d) 19
  34. 34.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) 21 (d) 54
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 2 (b) 3 (c) 4 (d) 5
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 4 (d) 3
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 9 (b) 12 (c) 11 (d) 10
  38. 38.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
  39. 39.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) 30 (b) 27 (c) 9 (d) 81
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 19 (d) 7

Answer key

  1. 18
  2. 4
  3. 45
  4. 297
  5. 12
  6. 127
  7. 19
  8. 37
  9. 519
  10. 30
  11. 54
  12. 17
  13. 234
  14. 133
  15. 6
  16. 20
  17. 21
  18. 155
  19. 14
  20. 8
  21. 14
  22. 3
  23. 7
  24. 20
  25. 20
  26. 163
  27. 42
  28. 6
  29. 6
  30. 143
  31. 72
  32. 95
  33. 57
  34. 18
  35. 4
  36. 3
  37. 11
  38. 60
  39. 27
  40. 18

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