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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 244 · 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 70? (a) 8 (b) 9 (c) 7 (d) 6
  2. 2.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 57? (a) 5 (b) 4 (c) 6 (d) 3
  4. 4.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 232 (d) 231
  5. 5.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 452 (c) 570 (d) 571
  6. 6.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
  7. 7.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) 198 (c) 69 (d) 22
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 18 (b) 9 (c) 19 (d) 20
  9. 9.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 230 (c) 228 (d) 238
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 7 (b) 19 (c) 17 (d) 18
  11. 11.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
  13. 13.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 126 (c) 134 (d) 125
  14. 14.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 278 (c) 300 (d) 309
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 18 (b) 16 (c) 17 (d) 7
  16. 16.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
  17. 17.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  18. 18.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 61 (b) 70 (c) 62 (d) 52
  19. 19.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 456 (c) 465 (d) 466
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 2 (b) 3 (c) 4 (d) 5
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 65? (a) 12 (b) 13 (c) 6 (d) 10
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 16 (b) 17 (c) 18 (d) 6
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 21 (d) 19
  24. 24.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  25. 25.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) 51 (b) 48 (c) 144 (d) 16
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 20 (d) 19
  27. 27.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 382 (c) 326 (d) 381
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 2 (b) 5 (c) 3 (d) 4
  29. 29.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  30. 30.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) 18 (b) 21 (c) 6 (d) 54
  31. 31.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 523 (c) 513 (d) 522
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 16 (b) 4 (c) 14 (d) 15
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 4 (b) 2 (c) 3 (d) 5
  34. 34.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 7 (b) 6 (c) 5 (d) 8
  36. 36.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) 171 (c) 57 (d) 19
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 85? (a) 8 (b) 18 (c) 19 (d) 20
  38. 38.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) 30 (b) 90 (c) 10 (d) 33
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 13 (b) 15 (c) 3 (d) 14
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 66? (a) 6 (b) 5 (c) 7 (d) 4

Answer key

  1. 8
  2. 7
  3. 5
  4. 231
  5. 570
  6. 137
  7. 66
  8. 19
  9. 237
  10. 18
  11. 2
  12. 9
  13. 125
  14. 309
  15. 17
  16. 27
  17. 8
  18. 61
  19. 465
  20. 4
  21. 12
  22. 17
  23. 20
  24. 4
  25. 48
  26. 19
  27. 381
  28. 4
  29. 8
  30. 18
  31. 522
  32. 15
  33. 4
  34. 3
  35. 7
  36. 57
  37. 19
  38. 30
  39. 14
  40. 6

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