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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 559 · 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 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 76 (c) 68 (d) 67
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 4 (b) 7 (c) 5 (d) 6
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 5 (b) 3 (c) 4 (d) 2
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 15 (b) 5 (c) 17 (d) 16
  5. 5.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 595 (b) 585 (c) 594 (d) 468
  6. 6.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) 51 (b) 144 (c) 16 (d) 48
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 17 (b) 18 (c) 7 (d) 19
  8. 8.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) 30 (c) 81 (d) 27
  9. 9.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) 8 (b) 24 (c) 72 (d) 27
  10. 10.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 18 (b) 6 (c) 16 (d) 17
  11. 11.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 184 (c) 183 (d) 192
  12. 12.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4
  13. 13.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
  14. 14.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 391 (b) 332 (c) 390 (d) 381
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 4 (b) 6 (c) 5 (d) 3
  16. 16.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
  18. 18.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  19. 19.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 59 (b) 60 (c) 50 (d) 68
  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) 72 (b) 75 (c) 216 (d) 24
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 5 (b) 4 (c) 3 (d) 2
  22. 22.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 7 (d) 9
  23. 23.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 81 (b) 90 (c) 72 (d) 82
  24. 24.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) 45 (b) 15 (c) 135 (d) 48
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 93? (a) 20 (b) 18 (c) 9 (d) 19
  26. 26.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 9 (d) 11
  27. 27.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 73 (c) 82 (d) 64
  28. 28.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 550 (c) 540 (d) 549
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 4 (b) 6 (c) 5 (d) 7
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 2 (b) 3 (c) 4 (d) 5
  31. 31.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) 99 (b) 33 (c) 11 (d) 36
  32. 32.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) 66 (c) 63 (d) 189
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 3 (b) 15 (c) 14 (d) 13
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 16 (b) 15 (c) 4 (d) 14
  35. 35.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 3 (d) 5
  37. 37.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  38. 38.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 444 (c) 549 (d) 559
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 7 (b) 18 (c) 19 (d) 17
  40. 40.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 8 (d) 10

Answer key

  1. 67
  2. 6
  3. 4
  4. 16
  5. 594
  6. 48
  7. 18
  8. 27
  9. 24
  10. 17
  11. 183
  12. 4
  13. 7
  14. 390
  15. 5
  16. 2
  17. 3
  18. 2
  19. 59
  20. 72
  21. 4
  22. 8
  23. 81
  24. 45
  25. 19
  26. 9
  27. 73
  28. 549
  29. 6
  30. 4
  31. 33
  32. 63
  33. 14
  34. 15
  35. 9
  36. 4
  37. 5
  38. 558
  39. 18
  40. 7

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