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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 981 · 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 1 written when you write all the numbers from 1 to 82? (a) 18 (b) 8 (c) 20 (d) 19
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 2 (b) 3 (c) 4 (d) 5
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 13 (b) 15 (c) 3 (d) 14
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 14 (b) 15 (c) 16 (d) 5
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 17 (b) 18 (c) 7 (d) 19
  6. 6.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  7. 7.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) 57 (b) 54 (c) 162 (d) 18
  8. 8.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 15 (b) 3 (c) 13 (d) 14
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 8 (b) 6 (c) 7 (d) 5
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 16 (b) 17 (c) 18 (d) 6
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 59? (a) 7 (b) 5 (c) 4 (d) 6
  13. 13.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) 24 (b) 63 (c) 21 (d) 7
  14. 14.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 7 (d) 14
  15. 15.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) 90 (b) 10 (c) 33 (d) 30
  16. 16.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  17. 17.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) 180 (c) 63 (d) 60
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 7 (b) 4 (c) 5 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  20. 20.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 564 (c) 573 (d) 574
  21. 21.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  22. 22.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) 6 (b) 54 (c) 21 (d) 18
  23. 23.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  24. 24.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 139 (b) 130 (c) 148 (d) 140
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 96? (a) 14 (b) 17 (c) 16 (d) 9
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 5 (b) 3 (c) 4 (d) 2
  27. 27.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 374 (b) 453 (c) 444 (d) 454
  28. 28.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 66 (c) 48 (d) 57
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 70? (a) 18 (b) 17 (c) 7 (d) 16
  30. 30.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  31. 31.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 62 (c) 53 (d) 54
  32. 32.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 8 (b) 18 (c) 20 (d) 19
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 9 (b) 8 (c) 6 (d) 7
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 55? (a) 5 (b) 6 (c) 3 (d) 4
  36. 36.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) 22 (b) 198 (c) 69 (d) 66
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 71? (a) 18 (b) 17 (c) 16 (d) 7
  38. 38.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 91 (c) 92 (d) 100
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 7 (b) 8 (c) 10 (d) 11
  40. 40.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 452 (b) 570 (c) 571 (d) 561

Answer key

  1. 19
  2. 4
  3. 14
  4. 15
  5. 18
  6. 7
  7. 54
  8. 9
  9. 14
  10. 7
  11. 17
  12. 6
  13. 21
  14. 6
  15. 30
  16. 4
  17. 60
  18. 6
  19. 5
  20. 573
  21. 3
  22. 18
  23. 2
  24. 139
  25. 16
  26. 4
  27. 453
  28. 57
  29. 17
  30. 6
  31. 53
  32. 7
  33. 19
  34. 8
  35. 5
  36. 66
  37. 17
  38. 91
  39. 10
  40. 570

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