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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 61 · 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 42? (a) 14 (b) 4 (c) 15 (d) 16
  2. 2.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 117 (c) 13 (d) 42
  3. 3.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 450 (c) 567 (d) 568
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 18 (b) 19 (c) 20 (d) 8
  5. 5.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) 45 (b) 48 (c) 15 (d) 135
  6. 6.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 6 (b) 7 (c) 9 (d) 8
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 19 (b) 20 (c) 21 (d) 9
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 18 (b) 20 (c) 8 (d) 19
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 18 (b) 17 (c) 16 (d) 7
  11. 11.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 19 (b) 20 (c) 9 (d) 21
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 95? (a) 20 (b) 18 (c) 19 (d) 9
  14. 14.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  15. 15.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
  16. 16.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) 45 (c) 18 (d) 15
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 3 (b) 6 (c) 4 (d) 5
  18. 18.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 17 (b) 19 (c) 18 (d) 8
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 7 (b) 11 (c) 8 (d) 10
  21. 21.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 8 (c) 27 (d) 72
  22. 22.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 456 (c) 382 (d) 466
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 17 (b) 18 (c) 7 (d) 19
  24. 24.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 417 (c) 418 (d) 350
  25. 25.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  26. 26.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 3 (d) 5
  27. 27.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 89 (c) 90 (d) 98
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 3 (b) 14 (c) 13 (d) 12
  29. 29.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 96 (c) 78 (d) 87
  30. 30.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) 48 (b) 16 (c) 51 (d) 144
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 18 (b) 16 (c) 17 (d) 6
  32. 32.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) 63 (d) 180
  33. 33.The numbers 17 to 25 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) 66 (d) 189
  34. 34.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 526 (b) 422 (c) 525 (d) 516
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 5 (b) 4 (c) 2 (d) 3
  36. 36.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  37. 37.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) 54 (b) 6 (c) 18 (d) 21
  38. 38.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 511 (b) 501 (c) 412 (d) 510
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 4 (b) 3 (c) 5 (d) 2
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 4 (b) 3 (c) 6 (d) 5

Answer key

  1. 15
  2. 39
  3. 567
  4. 19
  5. 45
  6. 3
  7. 8
  8. 20
  9. 19
  10. 17
  11. 8
  12. 20
  13. 19
  14. 5
  15. 42
  16. 15
  17. 5
  18. 2
  19. 18
  20. 10
  21. 24
  22. 465
  23. 18
  24. 417
  25. 9
  26. 4
  27. 89
  28. 13
  29. 87
  30. 48
  31. 17
  32. 60
  33. 63
  34. 525
  35. 4
  36. 7
  37. 18
  38. 510
  39. 4
  40. 5

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