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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 674 · 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 81? (a) 20 (b) 18 (c) 8 (d) 19
  2. 2.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
  3. 3.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 19 (b) 18 (c) 7 (d) 17
  5. 5.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) 516 (d) 525
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 16 (b) 15 (c) 5 (d) 17
  7. 7.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
  8. 8.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 122 (c) 114 (d) 113
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 17 (b) 16 (c) 6 (d) 18
  10. 10.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 37 (b) 38 (c) 46 (d) 28
  11. 11.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) 16 (d) 144
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 58? (a) 15 (b) 17 (c) 5 (d) 16
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 1 (b) 4 (c) 2 (d) 3
  14. 14.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 33 (c) 99 (d) 36
  15. 15.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  17. 17.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) 66 (c) 69 (d) 198
  18. 18.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) 5 (d) 15
  19. 19.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) 14 (c) 42 (d) 126
  20. 20.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) 21 (b) 18 (c) 6 (d) 54
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 21 (b) 9 (c) 19 (d) 20
  22. 22.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 16 (b) 18 (c) 6 (d) 17
  24. 24.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 69 (c) 23 (d) 72
  25. 25.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 8 (d) 10
  26. 26.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) 19 (c) 171 (d) 57
  27. 27.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 17 (b) 19 (c) 18 (d) 8
  29. 29.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 496 (c) 495 (d) 486
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 6 (b) 4 (c) 7 (d) 5
  31. 31.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) 62 (c) 52 (d) 70
  32. 32.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  33. 33.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) 7 (b) 24 (c) 21 (d) 63
  34. 34.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
  35. 35.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 468 (c) 390 (d) 477
  36. 36.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 4 (b) 2 (c) 3 (d) 5
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 4 (b) 6 (c) 3 (d) 5
  39. 39.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 17 (c) 51 (d) 54
  40. 40.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 47 (c) 56 (d) 48

Answer key

  1. 19
  2. 5
  3. 8
  4. 18
  5. 525
  6. 16
  7. 45
  8. 113
  9. 17
  10. 37
  11. 48
  12. 16
  13. 3
  14. 33
  15. 2
  16. 3
  17. 66
  18. 15
  19. 42
  20. 18
  21. 20
  22. 7
  23. 17
  24. 69
  25. 9
  26. 57
  27. 9
  28. 18
  29. 495
  30. 6
  31. 61
  32. 7
  33. 21
  34. 6
  35. 477
  36. 4
  37. 4
  38. 5
  39. 51
  40. 47

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