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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 218 · 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 58? (a) 17 (b) 5 (c) 15 (d) 16
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 15 (b) 14 (c) 16 (d) 4
  3. 3.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) 42 (b) 39 (c) 117 (d) 13
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 8 (b) 19 (c) 17 (d) 18
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  6. 6.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 51 (c) 42 (d) 60
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 14 (b) 16 (c) 4 (d) 15
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 16 (b) 4 (c) 15 (d) 14
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 15 (b) 16 (c) 14 (d) 5
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 14 (b) 16 (c) 15 (d) 4
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 6 (b) 5 (c) 4 (d) 3
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 18 (b) 17 (c) 19 (d) 7
  13. 13.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 423 (c) 414 (d) 354
  14. 14.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  15. 15.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) 36 (d) 99
  16. 16.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 6 (d) 15
  17. 17.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) 15 (b) 5 (c) 45 (d) 18
  18. 18.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 634 (b) 633 (c) 624 (d) 494
  19. 19.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 9 (b) 18 (c) 19 (d) 20
  21. 21.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) 198 (b) 69 (c) 66 (d) 22
  22. 22.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) 40 (c) 50 (d) 58
  23. 23.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) 27 (c) 81 (d) 30
  24. 24.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 294 (c) 334 (d) 324
  25. 25.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) 60 (d) 57
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 18 (b) 16 (c) 17 (d) 7
  27. 27.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 1 (b) 3 (c) 4 (d) 2
  29. 29.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  30. 30.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) 180 (b) 20 (c) 63 (d) 60
  31. 31.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
  32. 32.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  33. 33.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) 18 (b) 54 (c) 6 (d) 21
  34. 34.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 84 (c) 76 (d) 75
  35. 35.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 78? (a) 18 (b) 19 (c) 7 (d) 17
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 14 (b) 4 (c) 15 (d) 16
  38. 38.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 8 (d) 13
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 20 (b) 18 (c) 9 (d) 19
  40. 40.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) 33 (b) 90 (c) 30 (d) 10

Answer key

  1. 16
  2. 15
  3. 39
  4. 18
  5. 3
  6. 51
  7. 15
  8. 15
  9. 15
  10. 15
  11. 5
  12. 18
  13. 423
  14. 2
  15. 33
  16. 5
  17. 15
  18. 633
  19. 3
  20. 19
  21. 66
  22. 49
  23. 27
  24. 333
  25. 57
  26. 17
  27. 2
  28. 3
  29. 4
  30. 60
  31. 6
  32. 9
  33. 18
  34. 75
  35. 5
  36. 18
  37. 15
  38. 7
  39. 19
  40. 30

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