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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 301 · 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 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 500 (b) 642 (c) 643 (d) 633
  2. 2.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 216 (d) 225
  3. 3.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 63? (a) 8 (b) 11 (c) 10 (d) 6
  5. 5.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) 11 (c) 99 (d) 36
  6. 6.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 3 (b) 5 (c) 4 (d) 2
  8. 8.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) 162 (c) 57 (d) 54
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 18 (b) 19 (c) 20 (d) 8
  10. 10.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 494 (b) 634 (c) 633 (d) 624
  11. 11.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 218 (c) 219 (d) 210
  12. 12.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) 30 (b) 10 (c) 33 (d) 90
  13. 13.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
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 2 (b) 1 (c) 4 (d) 3
  15. 15.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) 180 (d) 20
  16. 16.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) 189 (c) 21 (d) 63
  17. 17.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) 216 (c) 24 (d) 72
  18. 18.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) 21 (b) 6 (c) 18 (d) 54
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 7 (b) 17 (c) 18 (d) 19
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 70? (a) 5 (b) 6 (c) 7 (d) 8
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 18 (b) 20 (c) 19 (d) 9
  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) 19 (b) 60 (c) 171 (d) 57
  24. 24.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 135 (b) 126 (c) 144 (d) 136
  25. 25.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) 63 (b) 24 (c) 7 (d) 21
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 14 (b) 12 (c) 13 (d) 3
  27. 27.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) 54 (b) 17 (c) 51 (d) 153
  28. 28.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) 24 (b) 8 (c) 72 (d) 27
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
  30. 30.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 110 (c) 92 (d) 101
  31. 31.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  32. 32.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 94 (c) 85 (d) 76
  33. 33.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 9 (b) 8 (c) 11 (d) 12
  35. 35.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 414 (c) 424 (d) 423
  36. 36.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  37. 37.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) 36 (b) 12 (c) 108 (d) 39
  38. 38.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
  39. 39.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  40. 40.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3

Answer key

  1. 642
  2. 225
  3. 3
  4. 10
  5. 33
  6. 4
  7. 4
  8. 54
  9. 19
  10. 633
  11. 219
  12. 30
  13. 39
  14. 3
  15. 60
  16. 63
  17. 72
  18. 18
  19. 18
  20. 7
  21. 7
  22. 19
  23. 57
  24. 135
  25. 21
  26. 13
  27. 51
  28. 24
  29. 6
  30. 101
  31. 5
  32. 85
  33. 6
  34. 11
  35. 423
  36. 2
  37. 36
  38. 69
  39. 9
  40. 2

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