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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 987 · 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.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) 6 (c) 21 (d) 54
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 4 (b) 2 (c) 5 (d) 3
  3. 3.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 525 (c) 422 (d) 526
  4. 4.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 109 (b) 100 (c) 110 (d) 118
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 4 (d) 5
  6. 6.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 16 (b) 17 (c) 18 (d) 7
  8. 8.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) 48 (c) 135 (d) 15
  9. 9.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) 162 (b) 18 (c) 57 (d) 54
  10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 60? (a) 4 (b) 7 (c) 5 (d) 6
  11. 11.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
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 18 (b) 9 (c) 19 (d) 20
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 58? (a) 4 (b) 3 (c) 6 (d) 5
  15. 15.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) 21 (b) 189 (c) 63 (d) 66
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 20 (b) 19 (c) 9 (d) 21
  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) 81 (c) 27 (d) 30
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 7 (d) 18
  19. 19.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 181 (b) 172 (c) 182 (d) 190
  20. 20.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  21. 21.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 17 (b) 15 (c) 16 (d) 5
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 60? (a) 5 (b) 8 (c) 6 (d) 7
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 4 (d) 1
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 65? (a) 16 (b) 17 (c) 18 (d) 6
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 3 (b) 6 (c) 4 (d) 5
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 18 (b) 8 (c) 19 (d) 17
  28. 28.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 472 (c) 600 (d) 601
  29. 29.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 53 (c) 54 (d) 44
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 94? (a) 19 (b) 20 (c) 21 (d) 9
  31. 31.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 12 (b) 13 (c) 3 (d) 14
  33. 33.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 338 (c) 400 (d) 390
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 6 (b) 17 (c) 18 (d) 16
  35. 35.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  36. 36.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 555 (c) 565 (d) 564
  37. 37.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 5 (b) 17 (c) 15 (d) 16
  39. 39.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 213 (b) 321 (c) 214 (d) 204
  40. 40.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) 39 (c) 108 (d) 36

Answer key

  1. 18
  2. 4
  3. 525
  4. 109
  5. 5
  6. 6
  7. 17
  8. 45
  9. 54
  10. 6
  11. 57
  12. 5
  13. 19
  14. 5
  15. 63
  16. 20
  17. 27
  18. 18
  19. 181
  20. 9
  21. 6
  22. 16
  23. 7
  24. 3
  25. 17
  26. 5
  27. 18
  28. 600
  29. 53
  30. 20
  31. 3
  32. 13
  33. 399
  34. 17
  35. 3
  36. 564
  37. 2
  38. 16
  39. 213
  40. 36

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