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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 477 · 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 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 387 (c) 378 (d) 330
  2. 2.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 322 (c) 375 (d) 376
  3. 3.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 474 (c) 475 (d) 465
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 3 (b) 4 (c) 2 (d) 5
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 6 (b) 17 (c) 18 (d) 16
  6. 6.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) 117 (b) 42 (c) 13 (d) 39
  7. 7.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 88 (c) 87 (d) 78
  8. 8.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 278 (c) 309 (d) 310
  9. 9.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
  10. 10.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 57 (b) 58 (c) 48 (d) 66
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 17 (b) 6 (c) 18 (d) 16
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 17 (b) 5 (c) 16 (d) 15
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 5 (b) 4 (c) 6 (d) 3
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 4 (b) 6 (c) 3 (d) 5
  15. 15.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) 45 (b) 18 (c) 5 (d) 15
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 4 (b) 12 (c) 11 (d) 10
  17. 17.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 136 (c) 135 (d) 144
  18. 18.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 9 (b) 20 (c) 21 (d) 19
  20. 20.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 43 (b) 44 (c) 34 (d) 52
  21. 21.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) 72 (c) 24 (d) 216
  22. 22.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 7 (d) 5
  23. 23.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 267 (c) 277 (d) 276
  24. 24.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) 45 (c) 126 (d) 14
  25. 25.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 129 (b) 130 (c) 120 (d) 138
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 92? (a) 18 (b) 19 (c) 9 (d) 20
  27. 27.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 8 (b) 17 (c) 19 (d) 18
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 9 (b) 21 (c) 19 (d) 20
  30. 30.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) 108 (c) 12 (d) 39
  31. 31.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 364 (c) 429 (d) 439
  32. 32.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) 69 (b) 72 (c) 207 (d) 23
  33. 33.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) 24 (b) 7 (c) 21 (d) 63
  34. 34.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 247 (b) 237 (c) 236 (d) 246
  35. 35.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 15 (d) 4
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 7 (b) 6 (c) 8 (d) 5
  37. 37.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) 72 (b) 8 (c) 24 (d) 27
  38. 38.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) 22 (b) 198 (c) 66 (d) 69
  39. 39.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  40. 40.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8

Answer key

  1. 387
  2. 375
  3. 474
  4. 4
  5. 17
  6. 39
  7. 87
  8. 309
  9. 2
  10. 57
  11. 17
  12. 16
  13. 5
  14. 5
  15. 15
  16. 11
  17. 135
  18. 7
  19. 20
  20. 43
  21. 72
  22. 6
  23. 276
  24. 42
  25. 129
  26. 19
  27. 2
  28. 18
  29. 20
  30. 36
  31. 438
  32. 69
  33. 21
  34. 246
  35. 5
  36. 7
  37. 24
  38. 66
  39. 7
  40. 9

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