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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 37 · 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 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 415 (b) 348 (c) 414 (d) 405
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 85? (a) 6 (b) 8 (c) 7 (d) 9
  3. 3.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 150 (c) 142 (d) 141
  4. 4.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 613 (c) 612 (d) 480
  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) 45 (b) 48 (c) 15 (d) 135
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  7. 7.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
  8. 8.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  9. 9.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) 13 (b) 117 (c) 42 (d) 39
  10. 10.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) 60 (c) 20 (d) 180
  11. 11.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) 39 (b) 108 (c) 12 (d) 36
  12. 12.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 59 (b) 68 (c) 50 (d) 60
  13. 13.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  14. 14.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  15. 15.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) 54 (b) 18 (c) 162 (d) 57
  16. 16.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 583 (c) 460 (d) 582
  17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 18 (b) 6 (c) 17 (d) 16
  18. 18.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  19. 19.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 166 (c) 156 (d) 165
  20. 20.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 158 (c) 168 (d) 167
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 13 (b) 15 (c) 14 (d) 3
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 3 (b) 1 (c) 4 (d) 2
  23. 23.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) 17 (b) 153 (c) 51 (d) 54
  24. 24.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) 60 (b) 19 (c) 57 (d) 171
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 12 (b) 14 (c) 3 (d) 13
  27. 27.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) 10 (b) 90 (c) 30 (d) 33
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 5 (b) 6 (c) 4 (d) 7
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 55? (a) 3 (b) 6 (c) 5 (d) 4
  30. 30.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 10 (d) 8
  31. 31.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 145 (b) 154 (c) 146 (d) 136
  32. 32.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) 27 (c) 9 (d) 30
  33. 33.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  34. 34.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 50? (a) 3 (b) 6 (c) 5 (d) 4
  36. 36.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 10 (d) 7
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 8 (b) 18 (c) 20 (d) 19
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 19 (b) 17 (c) 18 (d) 8
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 21 (b) 9 (c) 19 (d) 20
  40. 40.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 79 (b) 80 (c) 70 (d) 88

Answer key

  1. 414
  2. 8
  3. 141
  4. 612
  5. 45
  6. 9
  7. 69
  8. 3
  9. 39
  10. 60
  11. 36
  12. 59
  13. 8
  14. 4
  15. 54
  16. 582
  17. 17
  18. 2
  19. 165
  20. 167
  21. 14
  22. 3
  23. 51
  24. 57
  25. 7
  26. 13
  27. 30
  28. 6
  29. 5
  30. 9
  31. 145
  32. 27
  33. 5
  34. 5
  35. 5
  36. 6
  37. 19
  38. 18
  39. 20
  40. 79

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