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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 561 · 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 times is the digit 8 written when you write all the numbers from 1 to 49? (a) 5 (b) 6 (c) 4 (d) 3
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 5 (b) 3 (c) 2 (d) 4
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 17 (b) 16 (c) 15 (d) 5
  5. 5.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) 20 (c) 180 (d) 60
  6. 6.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) 72 (c) 207 (d) 69
  7. 7.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 4 (b) 6 (c) 7 (d) 3
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 17 (b) 7 (c) 18 (d) 19
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  11. 11.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) 27 (b) 30 (c) 81 (d) 9
  12. 12.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 447 (c) 448 (d) 438
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 40? (a) 6 (b) 4 (c) 5 (d) 3
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 36? (a) 4 (b) 3 (c) 1 (d) 2
  15. 15.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) 66 (b) 21 (c) 189 (d) 63
  16. 16.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 217 (c) 216 (d) 207
  17. 17.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 146 (c) 136 (d) 145
  18. 18.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 21 (b) 20 (c) 19 (d) 9
  20. 20.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) 24 (b) 72 (c) 75 (d) 216
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 86? (a) 18 (b) 20 (c) 19 (d) 8
  22. 22.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 390 (c) 468 (d) 478
  23. 23.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 474 (c) 483 (d) 484
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 16 (b) 14 (c) 15 (d) 5
  25. 25.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 520 (b) 418 (c) 519 (d) 510
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 94? (a) 9 (b) 20 (c) 18 (d) 19
  27. 27.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) 63 (b) 24 (c) 21 (d) 7
  28. 28.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) 45 (c) 36 (d) 46
  29. 29.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) 24 (b) 72 (c) 27 (d) 8
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 5 (b) 4 (c) 7 (d) 6
  31. 31.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) 15 (d) 5
  32. 32.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
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 20 (b) 9 (c) 21 (d) 19
  34. 34.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 124 (c) 116 (d) 115
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 9 (b) 19 (c) 18 (d) 16
  36. 36.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 388 (c) 387 (d) 378
  37. 37.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 174 (c) 164 (d) 173
  38. 38.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 8 (d) 7
  39. 39.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
  40. 40.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2

Answer key

  1. 5
  2. 4
  3. 6
  4. 16
  5. 60
  6. 69
  7. 8
  8. 6
  9. 18
  10. 7
  11. 27
  12. 447
  13. 5
  14. 3
  15. 63
  16. 216
  17. 145
  18. 4
  19. 20
  20. 72
  21. 19
  22. 477
  23. 483
  24. 15
  25. 519
  26. 19
  27. 21
  28. 45
  29. 24
  30. 6
  31. 15
  32. 11
  33. 20
  34. 115
  35. 18
  36. 387
  37. 173
  38. 8
  39. 48
  40. 2

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