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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 271 · 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.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 8 (d) 7
  2. 2.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) 108 (b) 39 (c) 36 (d) 12
  3. 3.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) 126 (b) 42 (c) 14 (d) 45
  4. 4.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 573 (c) 574 (d) 564
  5. 5.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 369 (c) 379 (d) 324
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 5 (b) 7 (c) 8 (d) 6
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 5 (d) 16
  8. 8.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 304 (c) 303 (d) 274
  9. 9.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) 13 (b) 117 (c) 42 (d) 39
  10. 10.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) 23 (b) 207 (c) 72 (d) 69
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 4 (b) 14 (c) 16 (d) 15
  12. 12.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) 45 (c) 135 (d) 15
  13. 13.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) 21 (b) 18 (c) 54 (d) 6
  14. 14.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 457 (b) 376 (c) 456 (d) 447
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 60? (a) 4 (b) 6 (c) 5 (d) 7
  16. 16.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) 27 (d) 24
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 16 (b) 6 (c) 17 (d) 18
  18. 18.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 224 (b) 219 (c) 229 (d) 228
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 90? (a) 19 (b) 20 (c) 18 (d) 9
  20. 20.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 84 (c) 83 (d) 74
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 69? (a) 8 (b) 5 (c) 7 (d) 6
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 17 (b) 15 (c) 16 (d) 5
  23. 23.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 267 (c) 268 (d) 250
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 17 (b) 5 (c) 15 (d) 16
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 40? (a) 3 (b) 6 (c) 4 (d) 5
  26. 26.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  27. 27.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 231 (c) 222 (d) 232
  28. 28.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) 48 (b) 16 (c) 144 (d) 51
  29. 29.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  30. 30.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  31. 31.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  32. 32.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 594 (c) 585 (d) 595
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 2 (b) 5 (c) 3 (d) 4
  34. 34.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) 9 (b) 81 (c) 30 (d) 27
  35. 35.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 67 (c) 68 (d) 58
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 6 (b) 4 (c) 7 (d) 5
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 5 (b) 2 (c) 3 (d) 4
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 9 (b) 4 (c) 6 (d) 8
  39. 39.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) 60 (d) 63
  40. 40.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 61 (b) 62 (c) 70 (d) 52

Answer key

  1. 8
  2. 36
  3. 42
  4. 573
  5. 378
  6. 7
  7. 16
  8. 303
  9. 39
  10. 69
  11. 15
  12. 45
  13. 18
  14. 456
  15. 6
  16. 24
  17. 17
  18. 228
  19. 19
  20. 83
  21. 7
  22. 16
  23. 267
  24. 16
  25. 5
  26. 5
  27. 231
  28. 48
  29. 9
  30. 2
  31. 6
  32. 594
  33. 4
  34. 27
  35. 67
  36. 6
  37. 4
  38. 8
  39. 60
  40. 61

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