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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 539 · 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 6 written when you write all the numbers from 1 to 81? (a) 18 (b) 8 (c) 19 (d) 17
  2. 2.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  3. 3.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) 189 (b) 66 (c) 63 (d) 21
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 65? (a) 7 (b) 5 (c) 4 (d) 6
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 6 (b) 5 (c) 4 (d) 3
  6. 6.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
  7. 7.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 49 (b) 50 (c) 58 (d) 40
  8. 8.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) 7 (c) 21 (d) 63
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 20 (b) 19 (c) 8 (d) 18
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 71? (a) 5 (b) 6 (c) 8 (d) 7
  11. 11.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
  12. 12.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) 18 (c) 45 (d) 15
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 15 (b) 4 (c) 14 (d) 16
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 14 (b) 13 (c) 3 (d) 15
  15. 15.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 553 (c) 440 (d) 552
  16. 16.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) 18 (c) 54 (d) 21
  17. 17.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 199 (c) 204 (d) 198
  18. 18.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 10 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  20. 20.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10
  21. 21.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) 33 (b) 99 (c) 11 (d) 36
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 5 (b) 4 (c) 2 (d) 3
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 6 (b) 16 (c) 17 (d) 15
  24. 24.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) 16 (c) 144 (d) 48
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 9 (b) 7 (c) 8 (d) 6
  26. 26.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) 8 (b) 72 (c) 24 (d) 27
  27. 27.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 90 (c) 99 (d) 108
  28. 28.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) 72 (d) 23
  29. 29.The numbers 20 to 28 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) 216 (c) 72 (d) 75
  30. 30.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
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  32. 32.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  33. 33.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 142 (c) 134 (d) 133
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 8 (b) 7 (c) 5 (d) 6
  35. 35.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 92? (a) 18 (b) 19 (c) 9 (d) 20
  37. 37.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 7 (d) 14
  38. 38.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
  39. 39.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) 171 (b) 19 (c) 57 (d) 60
  40. 40.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 101 (b) 110 (c) 92 (d) 102

Answer key

  1. 18
  2. 2
  3. 63
  4. 6
  5. 5
  6. 27
  7. 49
  8. 21
  9. 19
  10. 7
  11. 45
  12. 15
  13. 15
  14. 14
  15. 552
  16. 18
  17. 198
  18. 7
  19. 4
  20. 6
  21. 33
  22. 4
  23. 16
  24. 48
  25. 8
  26. 24
  27. 99
  28. 69
  29. 72
  30. 66
  31. 2
  32. 5
  33. 133
  34. 7
  35. 8
  36. 19
  37. 6
  38. 9
  39. 57
  40. 101

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