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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 468 · 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 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 262 (c) 285 (d) 276
  2. 2.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 628 (b) 627 (c) 618 (d) 490
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 19 (d) 21
  4. 4.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 20 (b) 8 (c) 19 (d) 18
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 54? (a) 3 (b) 5 (c) 4 (d) 6
  7. 7.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
  8. 8.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) 216 (b) 24 (c) 72 (d) 75
  9. 9.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 5 (d) 16
  10. 10.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 434 (c) 543 (d) 544
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 14 (b) 15 (c) 16 (d) 4
  12. 12.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) 90 (b) 33 (c) 10 (d) 30
  13. 13.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) 57 (d) 18
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 17 (b) 18 (c) 19 (d) 7
  15. 15.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 96 (c) 88 (d) 87
  16. 16.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) 117 (c) 42 (d) 13
  17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 1 (d) 3
  18. 18.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  19. 19.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 634 (b) 624 (c) 633 (d) 494
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 9 (b) 20 (c) 19 (d) 18
  21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 18 (b) 7 (c) 19 (d) 17
  22. 22.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) 12 (b) 108 (c) 36 (d) 39
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 4 (b) 2 (c) 3 (d) 5
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 5 (d) 4
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 3 (b) 5 (c) 4 (d) 2
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 17 (b) 7 (c) 19 (d) 18
  27. 27.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  28. 28.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 378 (c) 379 (d) 324
  29. 29.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) 60 (b) 57 (c) 19 (d) 171
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 18 (d) 19
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 19 (b) 18 (c) 20 (d) 8
  32. 32.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 408 (c) 504 (d) 505
  33. 33.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) 153 (c) 51 (d) 54
  34. 34.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  35. 35.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
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 63? (a) 10 (b) 8 (c) 11 (d) 6
  37. 37.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 18 (d) 3
  38. 38.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  39. 39.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  40. 40.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5

Answer key

  1. 285
  2. 627
  3. 20
  4. 8
  5. 19
  6. 5
  7. 60
  8. 72
  9. 4
  10. 543
  11. 15
  12. 30
  13. 54
  14. 18
  15. 87
  16. 39
  17. 3
  18. 4
  19. 633
  20. 19
  21. 18
  22. 36
  23. 4
  24. 5
  25. 4
  26. 18
  27. 5
  28. 378
  29. 57
  30. 19
  31. 19
  32. 504
  33. 51
  34. 7
  35. 45
  36. 10
  37. 2
  38. 6
  39. 9
  40. 5

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