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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 580 · 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 8 written when you write all the numbers from 1 to 45? (a) 5 (b) 2 (c) 4 (d) 3
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 7 (b) 19 (c) 17 (d) 18
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 8 (b) 18 (c) 17 (d) 19
  4. 4.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 123 (b) 132 (c) 114 (d) 124
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  6. 6.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 604 (c) 594 (d) 474
  7. 7.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  8. 8.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 477 (c) 390 (d) 478
  9. 9.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) 15 (c) 135 (d) 45
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 4 (d) 3
  11. 11.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 75? (a) 18 (b) 19 (c) 7 (d) 17
  13. 13.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 4 (b) 2 (c) 1 (d) 3
  15. 15.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 69 (c) 60 (d) 78
  16. 16.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 307 (c) 297 (d) 306
  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) 63 (b) 21 (c) 7 (d) 24
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 7 (b) 3 (c) 8 (d) 9
  19. 19.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) 18 (b) 45 (c) 15 (d) 5
  20. 20.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) 60 (b) 20 (c) 180 (d) 63
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 3 (b) 5 (c) 2 (d) 4
  22. 22.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) 42 (c) 126 (d) 14
  23. 23.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 561 (c) 571 (d) 452
  24. 24.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 304 (c) 274 (d) 303
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 90? (a) 20 (b) 19 (c) 18 (d) 9
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 2 (b) 1 (c) 3 (d) 4
  28. 28.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 12 (c) 108 (d) 39
  29. 29.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) 172 (c) 154 (d) 163
  30. 30.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 237 (c) 230 (d) 238
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  32. 32.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 150 (c) 132 (d) 141
  33. 33.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 564 (b) 448 (c) 555 (d) 565
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 7 (d) 19
  35. 35.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 3 (b) 2 (c) 5 (d) 4
  37. 37.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 322 (c) 376 (d) 375
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 5 (b) 8 (c) 6 (d) 7
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 18 (b) 19 (c) 8 (d) 20
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 97? (a) 21 (b) 9 (c) 19 (d) 20

Answer key

  1. 4
  2. 18
  3. 18
  4. 123
  5. 6
  6. 603
  7. 7
  8. 477
  9. 45
  10. 4
  11. 4
  12. 18
  13. 3
  14. 3
  15. 69
  16. 306
  17. 21
  18. 8
  19. 15
  20. 60
  21. 4
  22. 42
  23. 570
  24. 303
  25. 7
  26. 19
  27. 3
  28. 36
  29. 163
  30. 237
  31. 2
  32. 141
  33. 564
  34. 18
  35. 9
  36. 4
  37. 375
  38. 7
  39. 19
  40. 20

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