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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 380 · 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 16? (a) 2 (b) 4 (c) 17 (d) 3
  2. 2.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 143 (c) 152 (d) 144
  3. 3.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 205 (b) 204 (c) 195 (d) 208
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 7 (b) 18 (c) 19 (d) 17
  5. 5.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 7 (d) 6
  6. 6.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 331 (b) 330 (c) 292 (d) 321
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 19 (b) 18 (c) 20 (d) 9
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 13 (b) 10 (c) 8 (d) 12
  9. 9.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) 20 (c) 63 (d) 180
  10. 10.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  11. 11.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) 54 (c) 53 (d) 44
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 9 (b) 19 (c) 21 (d) 20
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 57? (a) 6 (b) 3 (c) 4 (d) 5
  14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 63? (a) 5 (b) 4 (c) 7 (d) 6
  15. 15.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 145 (c) 146 (d) 136
  16. 16.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
  17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 17 (b) 6 (c) 15 (d) 16
  18. 18.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 52 (c) 61 (d) 70
  19. 19.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) 22 (c) 198 (d) 66
  20. 20.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 5 (b) 3 (c) 4 (d) 2
  22. 22.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
  23. 23.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 15 (b) 3 (c) 13 (d) 14
  25. 25.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) 117 (b) 42 (c) 39 (d) 13
  26. 26.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) 36 (d) 108
  27. 27.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 3 (b) 15 (c) 14 (d) 13
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 20 (d) 21
  30. 30.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
  31. 31.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) 51 (b) 153 (c) 17 (d) 54
  32. 32.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) 19 (b) 57 (c) 171 (d) 60
  33. 33.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) 81 (b) 9 (c) 30 (d) 27
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 14 (b) 15 (c) 4 (d) 16
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 49? (a) 4 (b) 6 (c) 3 (d) 5
  36. 36.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 133 (b) 142 (c) 134 (d) 124
  37. 37.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) 216 (d) 72
  38. 38.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) 45 (b) 18 (c) 15 (d) 5
  39. 39.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  40. 40.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 186 (c) 177 (d) 168

Answer key

  1. 3
  2. 143
  3. 204
  4. 18
  5. 6
  6. 330
  7. 19
  8. 12
  9. 60
  10. 4
  11. 53
  12. 20
  13. 5
  14. 6
  15. 145
  16. 8
  17. 16
  18. 61
  19. 66
  20. 5
  21. 4
  22. 9
  23. 7
  24. 14
  25. 39
  26. 36
  27. 3
  28. 14
  29. 20
  30. 2
  31. 51
  32. 57
  33. 27
  34. 15
  35. 5
  36. 133
  37. 72
  38. 15
  39. 7
  40. 177

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