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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 247 · 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 7? (a) 6 (b) 7 (c) 8 (d) 10
  2. 2.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) 45 (c) 5 (d) 15
  3. 3.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) 42 (b) 45 (c) 126 (d) 14
  4. 4.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 24 (c) 27 (d) 8
  5. 5.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 132 (c) 142 (d) 141
  6. 6.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 104 (c) 95 (d) 86
  7. 7.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  8. 8.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  9. 9.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) 30 (b) 27 (c) 9 (d) 81
  10. 10.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
  11. 11.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) 33 (b) 99 (c) 11 (d) 36
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 4 (b) 2 (c) 3 (d) 5
  13. 13.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 11 (b) 10 (c) 9 (d) 12
  15. 15.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 1 (b) 2 (c) 4 (d) 3
  17. 17.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 16 (c) 144 (d) 51
  18. 18.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  19. 19.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) 23 (b) 72 (c) 207 (d) 69
  20. 20.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 30 (b) 48 (c) 39 (d) 40
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 17 (b) 7 (c) 18 (d) 19
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 3 (b) 4 (c) 2 (d) 1
  24. 24.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 48 (c) 47 (d) 56
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 9 (b) 20 (c) 21 (d) 19
  26. 26.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) 198 (b) 66 (c) 22 (d) 69
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 17 (b) 15 (c) 16 (d) 6
  28. 28.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) 66 (b) 21 (c) 63 (d) 189
  29. 29.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 13 (b) 15 (c) 3 (d) 14
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 6 (b) 4 (c) 5 (d) 3
  32. 32.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 139 (c) 130 (d) 140
  33. 33.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) 7 (b) 21 (c) 24 (d) 63
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 18 (b) 8 (c) 19 (d) 17
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 71? (a) 7 (b) 5 (c) 6 (d) 8
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 15 (b) 3 (c) 13 (d) 14
  37. 37.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) 60 (b) 63 (c) 180 (d) 20
  38. 38.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 272 (b) 291 (c) 301 (d) 300
  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.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 7 (b) 4 (c) 5 (d) 6

Answer key

  1. 7
  2. 15
  3. 42
  4. 24
  5. 141
  6. 95
  7. 4
  8. 5
  9. 27
  10. 9
  11. 33
  12. 4
  13. 6
  14. 11
  15. 8
  16. 3
  17. 48
  18. 5
  19. 69
  20. 39
  21. 18
  22. 3
  23. 3
  24. 47
  25. 20
  26. 66
  27. 16
  28. 63
  29. 9
  30. 14
  31. 5
  32. 139
  33. 21
  34. 18
  35. 7
  36. 14
  37. 60
  38. 300
  39. 7
  40. 6

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