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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 234 · 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 5 written when you write all the numbers from 1 to 92? (a) 20 (b) 19 (c) 18 (d) 9
  2. 2.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 85 (c) 76 (d) 94
  3. 3.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  4. 4.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 7 (b) 17 (c) 18 (d) 16
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 16 (b) 5 (c) 15 (d) 17
  7. 7.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 457 (c) 447 (d) 376
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 20 (d) 9
  9. 9.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) 9 (b) 81 (c) 27 (d) 30
  10. 10.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) 72 (b) 23 (c) 69 (d) 207
  11. 11.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 349 (c) 304 (d) 339
  12. 12.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  13. 13.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 66 (c) 74 (d) 65
  14. 14.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) 5 (b) 15 (c) 45 (d) 18
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 3 (b) 6 (c) 5 (d) 4
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 14 (b) 16 (c) 15 (d) 5
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 7 (b) 19 (c) 17 (d) 18
  18. 18.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 128 (c) 137 (d) 146
  19. 19.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 2 (d) 4
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 45? (a) 3 (b) 4 (c) 6 (d) 5
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 2 (b) 5 (c) 4 (d) 3
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 20 (b) 19 (c) 9 (d) 18
  24. 24.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) 20 (b) 63 (c) 60 (d) 180
  25. 25.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 156 (c) 155 (d) 146
  26. 26.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 98 (c) 116 (d) 107
  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) 232 (b) 240 (c) 231 (d) 241
  28. 28.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 11 (d) 10
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 8 (b) 19 (c) 18 (d) 17
  30. 30.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 140 (c) 131 (d) 122
  31. 31.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 92 (c) 102 (d) 101
  32. 32.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 8 (b) 5 (c) 7 (d) 6
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 17 (b) 6 (c) 15 (d) 16
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 71? (a) 6 (b) 8 (c) 5 (d) 7
  36. 36.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) 57 (c) 162 (d) 18
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 8 (b) 6 (c) 7 (d) 9
  38. 38.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 494 (b) 634 (c) 633 (d) 624
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 4 (b) 3 (c) 1 (d) 2
  40. 40.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 217 (c) 216 (d) 324

Answer key

  1. 19
  2. 85
  3. 6
  4. 2
  5. 17
  6. 16
  7. 456
  8. 20
  9. 27
  10. 69
  11. 348
  12. 8
  13. 65
  14. 15
  15. 5
  16. 15
  17. 18
  18. 137
  19. 3
  20. 5
  21. 4
  22. 3
  23. 19
  24. 60
  25. 155
  26. 107
  27. 240
  28. 9
  29. 18
  30. 131
  31. 101
  32. 9
  33. 7
  34. 16
  35. 7
  36. 54
  37. 8
  38. 633
  39. 3
  40. 216

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