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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 882 · 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.

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  1. 1.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 230 (c) 228 (d) 238
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 10 (b) 8 (c) 9 (d) 11
  3. 3.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 544 (b) 543 (c) 534 (d) 434
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 16 (b) 6 (c) 17 (d) 18
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 67? (a) 6 (b) 4 (c) 5 (d) 7
  6. 6.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) 30 (b) 9 (c) 27 (d) 81
  7. 7.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 262 (c) 276 (d) 286
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 17 (b) 6 (c) 18 (d) 16
  9. 9.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 15 (d) 6
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 17 (b) 5 (c) 16 (d) 15
  11. 11.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) 150 (c) 149 (d) 140
  12. 12.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 267 (c) 268 (d) 258
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 8 (b) 18 (c) 19 (d) 20
  14. 14.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 253 (b) 252 (c) 243 (d) 240
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 7 (b) 16 (c) 15 (d) 17
  16. 16.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 204 (c) 213 (d) 214
  17. 17.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
  18. 18.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  19. 19.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 169 (c) 170 (d) 160
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 17 (b) 18 (c) 19 (d) 7
  21. 21.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
  22. 22.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 67 (b) 76 (c) 68 (d) 58
  23. 23.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) 54 (b) 6 (c) 21 (d) 18
  24. 24.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 5 (d) 3
  25. 25.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 73 (c) 74 (d) 64
  26. 26.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  28. 28.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 113 (b) 122 (c) 104 (d) 114
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 18 (b) 17 (c) 6 (d) 16
  30. 30.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
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 16 (b) 18 (c) 17 (d) 7
  32. 32.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 5 (b) 17 (c) 16 (d) 15
  34. 34.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) 13 (c) 42 (d) 117
  35. 35.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  36. 36.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) 57 (b) 18 (c) 54 (d) 162
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 9 (b) 20 (c) 19 (d) 21
  38. 38.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 337 (b) 327 (c) 336 (d) 296
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 8 (b) 9 (c) 10 (d) 7
  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) 70 (b) 88 (c) 80 (d) 79

Answer key

  1. 237
  2. 10
  3. 543
  4. 17
  5. 6
  6. 27
  7. 285
  8. 17
  9. 5
  10. 16
  11. 149
  12. 267
  13. 19
  14. 252
  15. 16
  16. 213
  17. 42
  18. 8
  19. 169
  20. 18
  21. 69
  22. 67
  23. 18
  24. 4
  25. 73
  26. 3
  27. 9
  28. 113
  29. 17
  30. 60
  31. 17
  32. 6
  33. 16
  34. 39
  35. 7
  36. 54
  37. 20
  38. 336
  39. 9
  40. 79

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