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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 313 · 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 8 written when you write all the numbers from 1 to 95? (a) 18 (b) 20 (c) 9 (d) 19
  2. 2.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
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 6 (b) 17 (c) 16 (d) 15
  4. 4.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 36 (c) 39 (d) 108
  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) 15 (c) 48 (d) 135
  6. 6.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 47 (c) 48 (d) 38
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 14 (b) 16 (c) 15 (d) 4
  8. 8.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 81 (c) 82 (d) 72
  9. 9.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 55 (c) 64 (d) 56
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 4 (b) 9 (c) 6 (d) 8
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 15 (b) 4 (c) 16 (d) 14
  12. 12.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1
  13. 13.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) 117 (c) 13 (d) 39
  14. 14.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  15. 15.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) 54 (b) 162 (c) 57 (d) 18
  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) 45 (b) 18 (c) 15 (d) 5
  17. 17.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
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 6 (b) 17 (c) 15 (d) 16
  19. 19.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 565 (b) 448 (c) 555 (d) 564
  20. 20.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 6 (b) 18 (c) 17 (d) 16
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 4 (b) 3 (c) 5 (d) 6
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 3 (b) 4 (c) 6 (d) 5
  25. 25.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) 6 (c) 54 (d) 18
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 14 (b) 13 (c) 4 (d) 15
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 4 (d) 3
  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) 69 (b) 72 (c) 207 (d) 23
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 6 (b) 16 (c) 17 (d) 18
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 7 (b) 6 (c) 4 (d) 5
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 18 (b) 6 (c) 16 (d) 17
  32. 32.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) 57 (b) 60 (c) 171 (d) 19
  33. 33.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) 99 (b) 11 (c) 36 (d) 33
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 3 (b) 5 (c) 2 (d) 4
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 19 (b) 8 (c) 17 (d) 18
  36. 36.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 7 (d) 12
  37. 37.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 236 (c) 246 (d) 247
  38. 38.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 6 (b) 5 (c) 4 (d) 3
  40. 40.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 411 (c) 402 (d) 346

Answer key

  1. 19
  2. 21
  3. 16
  4. 36
  5. 45
  6. 47
  7. 15
  8. 81
  9. 55
  10. 8
  11. 15
  12. 2
  13. 39
  14. 8
  15. 54
  16. 15
  17. 27
  18. 16
  19. 564
  20. 2
  21. 17
  22. 5
  23. 3
  24. 5
  25. 18
  26. 14
  27. 4
  28. 69
  29. 17
  30. 6
  31. 17
  32. 57
  33. 33
  34. 4
  35. 18
  36. 8
  37. 246
  38. 9
  39. 5
  40. 411

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