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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 174 · 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 two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  2. 2.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) 10 (c) 30 (d) 90
  3. 3.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 634 (c) 494 (d) 624
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 3 (b) 14 (c) 13 (d) 15
  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) 15 (b) 135 (c) 45 (d) 48
  6. 6.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
  7. 7.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 17 (b) 18 (c) 6 (d) 16
  9. 9.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 10 (b) 9 (c) 12 (d) 13
  11. 11.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) 30 (c) 27 (d) 81
  12. 12.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
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 7 (b) 6 (c) 5 (d) 8
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 3 (d) 4
  15. 15.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 460 (c) 573 (d) 583
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 20 (b) 19 (c) 8 (d) 18
  17. 17.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 640 (c) 639 (d) 498
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 96? (a) 21 (b) 19 (c) 20 (d) 9
  19. 19.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  20. 20.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 222 (c) 231 (d) 226
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 3 (b) 15 (c) 13 (d) 14
  23. 23.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) 18 (b) 54 (c) 162 (d) 57
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 2 (b) 3 (c) 1 (d) 4
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 1 (b) 2 (c) 4 (d) 3
  26. 26.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 259 (b) 249 (c) 258 (d) 244
  27. 27.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) 69 (b) 66 (c) 22 (d) 198
  28. 28.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
  29. 29.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  30. 30.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 122 (c) 113 (d) 114
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 18 (b) 8 (c) 19 (d) 20
  32. 32.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) 50 (d) 41
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 4 (b) 3 (c) 1 (d) 2
  34. 34.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 2 (b) 1 (c) 4 (d) 3
  36. 36.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 280 (c) 258 (d) 270
  37. 37.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) 18 (b) 5 (c) 15 (d) 45
  38. 38.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 17 (c) 54 (d) 51
  39. 39.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  40. 40.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5

Answer key

  1. 5
  2. 30
  3. 633
  4. 14
  5. 45
  6. 42
  7. 8
  8. 17
  9. 5
  10. 12
  11. 27
  12. 60
  13. 7
  14. 4
  15. 582
  16. 19
  17. 639
  18. 20
  19. 9
  20. 231
  21. 19
  22. 14
  23. 54
  24. 3
  25. 3
  26. 258
  27. 66
  28. 33
  29. 2
  30. 113
  31. 19
  32. 41
  33. 3
  34. 3
  35. 3
  36. 279
  37. 15
  38. 51
  39. 4
  40. 6

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