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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 424 · 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 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 132 (c) 124 (d) 123
  2. 2.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 8 (d) 9
  3. 3.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  4. 4.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) 36 (b) 33 (c) 11 (d) 99
  5. 5.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 28 (b) 46 (c) 38 (d) 37
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 57? (a) 5 (b) 14 (c) 13 (d) 15
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 15 (b) 17 (c) 16 (d) 7
  8. 8.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  9. 9.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) 21 (b) 66 (c) 189 (d) 63
  10. 10.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 8 (b) 18 (c) 19 (d) 17
  12. 12.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 92? (a) 19 (b) 20 (c) 18 (d) 9
  14. 14.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) 14 (c) 45 (d) 126
  15. 15.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) 36 (c) 39 (d) 108
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 17 (b) 18 (c) 7 (d) 16
  17. 17.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) 54 (d) 18
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 2 (b) 5 (c) 4 (d) 3
  19. 19.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) 21 (b) 63 (c) 24 (d) 7
  20. 20.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) 54 (d) 51
  21. 21.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 4 (b) 15 (c) 16 (d) 14
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 8 (d) 17
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 8 (b) 18 (c) 19 (d) 20
  26. 26.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) 15 (d) 5
  27. 27.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 70 (c) 69 (d) 60
  28. 28.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) 20 (b) 180 (c) 63 (d) 60
  29. 29.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 164 (c) 182 (d) 173
  30. 30.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 535 (b) 534 (c) 428 (d) 525
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 4 (b) 3 (c) 5 (d) 6
  32. 32.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  33. 33.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 331 (c) 321 (d) 330
  34. 34.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 225 (b) 216 (c) 226 (d) 222
  35. 35.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 105 (b) 96 (c) 106 (d) 114
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 20 (d) 19
  37. 37.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 120 (c) 129 (d) 138
  38. 38.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 206 (c) 202 (d) 201
  39. 39.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 517 (b) 416 (c) 507 (d) 516
  40. 40.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 252 (c) 271 (d) 270

Answer key

  1. 123
  2. 8
  3. 9
  4. 33
  5. 37
  6. 14
  7. 16
  8. 4
  9. 63
  10. 6
  11. 18
  12. 3
  13. 19
  14. 42
  15. 36
  16. 17
  17. 18
  18. 4
  19. 21
  20. 51
  21. 6
  22. 2
  23. 15
  24. 18
  25. 19
  26. 15
  27. 69
  28. 60
  29. 173
  30. 534
  31. 5
  32. 5
  33. 330
  34. 225
  35. 105
  36. 20
  37. 129
  38. 201
  39. 516
  40. 270

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