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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 633 · 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.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 327 (c) 290 (d) 328
  2. 2.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  3. 3.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) 23 (c) 69 (d) 72
  4. 4.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) 75 (b) 24 (c) 72 (d) 216
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 17 (b) 18 (c) 16 (d) 7
  6. 6.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 7 (b) 4 (c) 6 (d) 5
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 13 (b) 15 (c) 3 (d) 14
  9. 9.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) 126 (b) 14 (c) 42 (d) 45
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 15 (b) 16 (c) 4 (d) 14
  11. 11.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) 13 (c) 39 (d) 117
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 1 (b) 2 (c) 4 (d) 3
  13. 13.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  14. 14.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
  15. 15.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 143 (c) 134 (d) 152
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 18 (b) 19 (c) 20 (d) 8
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 94? (a) 14 (b) 12 (c) 9 (d) 15
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 21 (b) 20 (c) 19 (d) 9
  19. 19.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 10 (d) 8
  20. 20.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
  21. 21.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) 60 (d) 63
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 6 (b) 4 (c) 5 (d) 3
  24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 2 (b) 5 (c) 4 (d) 3
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 3 (b) 4 (c) 2 (d) 5
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 3 (b) 1 (c) 4 (d) 2
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 4 (b) 6 (c) 5 (d) 7
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 19 (b) 20 (c) 8 (d) 18
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  30. 30.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  31. 31.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
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 11 (b) 14 (c) 8 (d) 13
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 5 (b) 4 (c) 6 (d) 7
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 18 (d) 8
  35. 35.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 310 (c) 357 (d) 358
  36. 36.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 373 (b) 372 (c) 363 (d) 320
  37. 37.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 73? (a) 16 (b) 7 (c) 18 (d) 17
  39. 39.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  40. 40.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 91 (b) 82 (c) 100 (d) 92

Answer key

  1. 327
  2. 8
  3. 69
  4. 72
  5. 17
  6. 3
  7. 6
  8. 14
  9. 42
  10. 15
  11. 39
  12. 3
  13. 4
  14. 18
  15. 143
  16. 19
  17. 14
  18. 20
  19. 7
  20. 5
  21. 60
  22. 2
  23. 5
  24. 4
  25. 4
  26. 3
  27. 6
  28. 19
  29. 6
  30. 6
  31. 21
  32. 13
  33. 6
  34. 18
  35. 357
  36. 372
  37. 9
  38. 17
  39. 9
  40. 91

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