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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 266 · 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 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 196 (b) 202 (c) 186 (d) 195
  2. 2.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 604 (b) 474 (c) 603 (d) 594
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 18 (b) 19 (c) 7 (d) 17
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 7 (d) 18
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 2 (d) 1
  6. 6.The numbers 12 to 20 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) 144 (c) 16 (d) 48
  7. 7.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) 15 (b) 135 (c) 48 (d) 45
  8. 8.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
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 18 (b) 6 (c) 17 (d) 16
  10. 10.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 255 (c) 256 (d) 242
  11. 11.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 352 (c) 342 (d) 351
  12. 12.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 334 (c) 333 (d) 324
  13. 13.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) 72 (b) 69 (c) 207 (d) 23
  14. 14.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 7 (d) 9
  15. 15.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) 198 (b) 69 (c) 66 (d) 22
  16. 16.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  17. 17.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) 30 (d) 9
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 9 (d) 20
  19. 19.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  20. 20.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
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 88? (a) 19 (b) 18 (c) 8 (d) 20
  22. 22.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 7 (d) 8
  23. 23.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 46 (c) 36 (d) 45
  24. 24.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 600 (b) 591 (c) 472 (d) 601
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 20 (b) 8 (c) 19 (d) 18
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 17 (d) 19
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 5 (b) 17 (c) 15 (d) 16
  29. 29.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 146 (c) 164 (d) 155
  30. 30.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) 14 (b) 45 (c) 42 (d) 126
  31. 31.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 30 (b) 40 (c) 39 (d) 48
  32. 32.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 252 (c) 261 (d) 262
  33. 33.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 84? (a) 18 (b) 20 (c) 19 (d) 8
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 17 (b) 15 (c) 16 (d) 5
  36. 36.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) 15 (b) 45 (c) 18 (d) 5
  37. 37.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) 153 (b) 17 (c) 54 (d) 51
  38. 38.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) 63 (b) 189 (c) 21 (d) 66
  39. 39.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
  40. 40.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7

Answer key

  1. 195
  2. 603
  3. 18
  4. 18
  5. 3
  6. 48
  7. 45
  8. 72
  9. 17
  10. 255
  11. 351
  12. 333
  13. 69
  14. 8
  15. 66
  16. 4
  17. 27
  18. 20
  19. 5
  20. 33
  21. 19
  22. 7
  23. 45
  24. 600
  25. 19
  26. 18
  27. 9
  28. 16
  29. 155
  30. 42
  31. 39
  32. 261
  33. 3
  34. 19
  35. 16
  36. 15
  37. 51
  38. 63
  39. 4
  40. 7

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