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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 342 · 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.The numbers 6 to 14 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) 10 (c) 90 (d) 30
  2. 2.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 260 (b) 273 (c) 282 (d) 283
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  4. 4.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  5. 5.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 138 (c) 137 (d) 128
  6. 6.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 404 (b) 489 (c) 498 (d) 499
  7. 7.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) 68 (c) 76 (d) 58
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 20 (b) 9 (c) 19 (d) 21
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 10 (b) 7 (c) 9 (d) 6
  10. 10.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 414 (c) 415 (d) 405
  11. 11.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
  12. 12.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) 42 (c) 126 (d) 45
  13. 13.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) 48 (b) 15 (c) 45 (d) 135
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 17 (b) 16 (c) 18 (d) 6
  15. 15.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 279 (c) 280 (d) 258
  16. 16.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  17. 17.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) 162 (b) 54 (c) 18 (d) 57
  18. 18.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 367 (b) 316 (c) 357 (d) 366
  19. 19.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 559 (c) 558 (d) 549
  20. 20.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) 69 (c) 23 (d) 72
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 94? (a) 18 (b) 19 (c) 20 (d) 9
  22. 22.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  23. 23.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 74 (c) 56 (d) 65
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 17 (b) 7 (c) 19 (d) 18
  25. 25.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 8 (b) 18 (c) 20 (d) 19
  27. 27.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) 5 (c) 18 (d) 45
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 17 (b) 15 (c) 16 (d) 5
  29. 29.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) 144 (b) 16 (c) 51 (d) 48
  30. 30.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) 66 (c) 69 (d) 198
  31. 31.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 17 (b) 16 (c) 18 (d) 6
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 17 (b) 15 (c) 16 (d) 6
  34. 34.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) 54 (c) 51 (d) 153
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 17 (b) 8 (c) 18 (d) 19
  36. 36.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 242 (c) 246 (d) 255
  37. 37.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 60 (c) 19 (d) 57
  38. 38.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) 11 (c) 99 (d) 33
  39. 39.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 96 (c) 105 (d) 106
  40. 40.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 7 (d) 5

Answer key

  1. 30
  2. 282
  3. 5
  4. 4
  5. 137
  6. 498
  7. 67
  8. 20
  9. 9
  10. 414
  11. 63
  12. 42
  13. 45
  14. 17
  15. 279
  16. 9
  17. 54
  18. 366
  19. 558
  20. 69
  21. 19
  22. 4
  23. 65
  24. 18
  25. 9
  26. 19
  27. 15
  28. 16
  29. 48
  30. 66
  31. 6
  32. 17
  33. 16
  34. 51
  35. 18
  36. 255
  37. 57
  38. 33
  39. 105
  40. 6

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