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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 206 · 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 85? (a) 15 (b) 12 (c) 8 (d) 14
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 4 (b) 5 (c) 6 (d) 3
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 3 (b) 15 (c) 14 (d) 13
  4. 4.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) 63 (b) 20 (c) 60 (d) 180
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 14 (b) 16 (c) 15 (d) 5
  6. 6.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 18 (b) 8 (c) 17 (d) 19
  8. 8.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) 216 (b) 75 (c) 72 (d) 24
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 19 (d) 21
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 18 (b) 17 (c) 15 (d) 9
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 1 (d) 2
  14. 14.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 42 (c) 41 (d) 50
  15. 15.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 15 (b) 14 (c) 5 (d) 16
  17. 17.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 5 (d) 16
  18. 18.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 194 (c) 185 (d) 186
  19. 19.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 266 (b) 282 (c) 292 (d) 291
  20. 20.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) 63 (c) 66 (d) 21
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 16 (b) 18 (c) 7 (d) 17
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 18 (b) 6 (c) 17 (d) 16
  23. 23.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) 19 (d) 171
  24. 24.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 457 (b) 456 (c) 447 (d) 376
  25. 25.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) 135 (b) 15 (c) 48 (d) 45
  26. 26.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 3 (b) 4 (c) 2 (d) 5
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 6 (b) 5 (c) 4 (d) 7
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 19 (b) 18 (c) 7 (d) 17
  30. 30.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 5 (b) 15 (c) 14 (d) 16
  32. 32.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 589 (b) 464 (c) 588 (d) 579
  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) 36 (b) 11 (c) 33 (d) 99
  34. 34.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
  35. 35.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
  36. 36.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 252 (c) 271 (d) 270
  37. 37.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) 14 (b) 42 (c) 45 (d) 126
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 12 (b) 3 (c) 11 (d) 13
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 8 (b) 7 (c) 5 (d) 6
  40. 40.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) 54 (b) 21 (c) 6 (d) 18

Answer key

  1. 14
  2. 5
  3. 14
  4. 60
  5. 15
  6. 2
  7. 18
  8. 72
  9. 20
  10. 7
  11. 17
  12. 5
  13. 3
  14. 41
  15. 8
  16. 15
  17. 4
  18. 185
  19. 291
  20. 63
  21. 17
  22. 17
  23. 57
  24. 456
  25. 45
  26. 3
  27. 4
  28. 6
  29. 18
  30. 8
  31. 15
  32. 588
  33. 33
  34. 69
  35. 9
  36. 270
  37. 42
  38. 12
  39. 7
  40. 18

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