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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 297 · 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 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 157 (c) 158 (d) 148
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 14 (b) 16 (c) 4 (d) 15
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 19 (b) 20 (c) 21 (d) 9
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 7 (d) 18
  5. 5.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) 6 (b) 18 (c) 21 (d) 54
  6. 6.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
  7. 7.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
  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) 57 (c) 54 (d) 162
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 6 (b) 18 (c) 16 (d) 17
  10. 10.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) 30 (c) 9 (d) 27
  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.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 140 (c) 150 (d) 149
  13. 13.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) 21 (d) 7
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 7 (d) 8
  15. 15.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 16 (b) 15 (c) 14 (d) 4
  17. 17.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 154 (c) 153 (d) 144
  18. 18.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) 63 (c) 66 (d) 189
  19. 19.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 346 (c) 302 (d) 336
  20. 20.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 595 (c) 594 (d) 468
  21. 21.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 156 (c) 155 (d) 164
  22. 22.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 339 (c) 304 (d) 348
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 3 (b) 4 (c) 5 (d) 2
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 8 (b) 6 (c) 5 (d) 7
  25. 25.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 16 (b) 6 (c) 18 (d) 17
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 16 (b) 18 (c) 7 (d) 17
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 1 (b) 4 (c) 2 (d) 3
  30. 30.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 508 (b) 507 (c) 498 (d) 410
  31. 31.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
  32. 32.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 16 (b) 18 (c) 17 (d) 6
  34. 34.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) 126 (d) 45
  35. 35.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  36. 36.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) 39 (b) 117 (c) 42 (d) 13
  37. 37.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 9 (d) 20
  39. 39.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
  40. 40.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) 76 (c) 85 (d) 94

Answer key

  1. 157
  2. 15
  3. 20
  4. 18
  5. 18
  6. 60
  7. 15
  8. 54
  9. 17
  10. 27
  11. 33
  12. 149
  13. 21
  14. 7
  15. 9
  16. 15
  17. 153
  18. 63
  19. 345
  20. 594
  21. 155
  22. 348
  23. 4
  24. 7
  25. 3
  26. 17
  27. 2
  28. 17
  29. 3
  30. 507
  31. 8
  32. 6
  33. 17
  34. 42
  35. 5
  36. 39
  37. 3
  38. 20
  39. 18
  40. 85

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