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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 385 · 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 2 written when you write all the numbers from 1 to 94? (a) 19 (b) 9 (c) 21 (d) 20
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 18 (b) 7 (c) 19 (d) 17
  3. 3.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  5. 5.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
  6. 6.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) 126 (b) 14 (c) 42 (d) 45
  7. 7.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 471 (c) 462 (d) 386
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 3 (b) 15 (c) 13 (d) 14
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 7 (b) 8 (c) 6 (d) 5
  10. 10.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) 135 (b) 48 (c) 45 (d) 15
  11. 11.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
  12. 12.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) 108 (b) 39 (c) 36 (d) 12
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 4 (b) 3 (c) 2 (d) 5
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 5 (b) 7 (c) 8 (d) 6
  15. 15.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) 69 (b) 198 (c) 22 (d) 66
  16. 16.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 9 (d) 10
  17. 17.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 93? (a) 19 (b) 18 (c) 9 (d) 20
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 8 (b) 19 (c) 20 (d) 18
  20. 20.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 144 (c) 134 (d) 143
  21. 21.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 333 (c) 300 (d) 343
  22. 22.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 432 (c) 541 (d) 540
  23. 23.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 30 (b) 40 (c) 39 (d) 48
  24. 24.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 355 (c) 345 (d) 308
  25. 25.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 10 (d) 6
  26. 26.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 505 (b) 408 (c) 495 (d) 504
  27. 27.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 486 (c) 622 (d) 612
  28. 28.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  30. 30.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 367 (c) 357 (d) 316
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 6 (b) 5 (c) 4 (d) 7
  32. 32.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 1 (b) 3 (c) 2 (d) 4
  34. 34.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) 30 (d) 27
  35. 35.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 589 (b) 588 (c) 579 (d) 464
  36. 36.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 4 (b) 5 (c) 6 (d) 7
  38. 38.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 149 (c) 140 (d) 150
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 8 (b) 17 (c) 19 (d) 18
  40. 40.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 286 (c) 322 (d) 321

Answer key

  1. 20
  2. 18
  3. 4
  4. 4
  5. 60
  6. 42
  7. 471
  8. 14
  9. 7
  10. 45
  11. 6
  12. 36
  13. 4
  14. 7
  15. 66
  16. 8
  17. 2
  18. 19
  19. 19
  20. 143
  21. 342
  22. 540
  23. 39
  24. 354
  25. 7
  26. 504
  27. 621
  28. 3
  29. 9
  30. 366
  31. 6
  32. 8
  33. 3
  34. 27
  35. 588
  36. 5
  37. 6
  38. 149
  39. 18
  40. 321

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