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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 647 · 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 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) 189 (b) 21 (c) 66 (d) 63
  2. 2.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) 5 (c) 18 (d) 15
  3. 3.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 457 (c) 447 (d) 376
  4. 4.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) 16 (b) 51 (c) 144 (d) 48
  5. 5.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 306 (c) 307 (d) 276
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 3 (b) 5 (c) 2 (d) 4
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 15 (b) 14 (c) 4 (d) 16
  8. 8.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 250 (c) 240 (d) 249
  9. 9.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 3 (b) 15 (c) 13 (d) 14
  11. 11.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 63 (b) 54 (c) 64 (d) 72
  12. 12.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 3 (b) 5 (c) 2 (d) 4
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 17 (b) 18 (c) 7 (d) 19
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 8 (b) 6 (c) 5 (d) 7
  16. 16.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) 6 (b) 54 (c) 18 (d) 21
  17. 17.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 637 (b) 636 (c) 496 (d) 627
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 3 (b) 5 (c) 4 (d) 2
  19. 19.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 96 (c) 104 (d) 95
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 8 (b) 11 (c) 10 (d) 5
  21. 21.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
  22. 22.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  23. 23.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) 180 (b) 63 (c) 20 (d) 60
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 15 (b) 16 (c) 14 (d) 4
  25. 25.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  26. 26.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) 64 (d) 82
  27. 27.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 600 (c) 609 (d) 610
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 15 (b) 17 (c) 16 (d) 6
  29. 29.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 404 (c) 499 (d) 489
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 7 (b) 19 (c) 17 (d) 18
  31. 31.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 16 (b) 14 (c) 5 (d) 15
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 15 (b) 4 (c) 16 (d) 14
  34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 14 (b) 13 (c) 3 (d) 15
  35. 35.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 85? (a) 20 (b) 8 (c) 18 (d) 19
  37. 37.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) 198 (b) 22 (c) 69 (d) 66
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 5 (b) 3 (c) 6 (d) 4
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 75? (a) 7 (b) 17 (c) 18 (d) 19
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 17 (b) 19 (c) 7 (d) 18

Answer key

  1. 63
  2. 15
  3. 456
  4. 48
  5. 306
  6. 4
  7. 15
  8. 249
  9. 3
  10. 14
  11. 63
  12. 5
  13. 4
  14. 18
  15. 7
  16. 18
  17. 636
  18. 4
  19. 95
  20. 10
  21. 4
  22. 9
  23. 60
  24. 15
  25. 2
  26. 73
  27. 609
  28. 16
  29. 498
  30. 18
  31. 6
  32. 15
  33. 15
  34. 14
  35. 2
  36. 19
  37. 66
  38. 5
  39. 18
  40. 18

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