← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 524 · 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 3 written when you write all the numbers from 1 to 30? (a) 5 (b) 3 (c) 4 (d) 2
  2. 2.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) 63 (c) 66 (d) 21
  3. 3.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) 64 (c) 54 (d) 72
  4. 4.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 7 (b) 16 (c) 18 (d) 17
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 3 (b) 4 (c) 5 (d) 2
  7. 7.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
  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) 30 (b) 27 (c) 81 (d) 9
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 55? (a) 3 (b) 6 (c) 4 (d) 5
  10. 10.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
  11. 11.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) 15 (c) 5 (d) 18
  12. 12.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) 82 (d) 72
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 19 (b) 20 (c) 21 (d) 9
  14. 14.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) 10 (b) 33 (c) 90 (d) 30
  15. 15.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 441 (c) 442 (d) 366
  16. 16.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 565 (c) 555 (d) 564
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 18 (b) 19 (c) 8 (d) 17
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 17 (b) 6 (c) 16 (d) 15
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 4 (b) 6 (c) 5 (d) 7
  20. 20.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) 489 (c) 499 (d) 404
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 5 (b) 3 (c) 2 (d) 4
  22. 22.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 46 (c) 37 (d) 28
  23. 23.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 114 (c) 106 (d) 105
  24. 24.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
  25. 25.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 619 (b) 609 (c) 618 (d) 484
  26. 26.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 3 (b) 15 (c) 14 (d) 13
  28. 28.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) 42 (b) 117 (c) 13 (d) 39
  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) 8 (b) 72 (c) 24 (d) 27
  30. 30.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) 63 (c) 60 (d) 180
  31. 31.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) 7 (d) 21
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 7 (b) 17 (c) 16 (d) 18
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 1 (b) 2 (c) 4 (d) 3
  34. 34.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 75 (c) 84 (d) 66
  35. 35.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) 45 (b) 126 (c) 42 (d) 14
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 84? (a) 20 (b) 8 (c) 18 (d) 19
  37. 37.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 14 (d) 7
  38. 38.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) 11 (c) 36 (d) 33
  39. 39.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 17 (b) 16 (c) 15 (d) 5

Answer key

  1. 4
  2. 63
  3. 63
  4. 5
  5. 17
  6. 4
  7. 2
  8. 27
  9. 5
  10. 8
  11. 15
  12. 81
  13. 20
  14. 30
  15. 441
  16. 564
  17. 18
  18. 16
  19. 6
  20. 498
  21. 4
  22. 37
  23. 105
  24. 9
  25. 618
  26. 4
  27. 14
  28. 39
  29. 24
  30. 60
  31. 21
  32. 17
  33. 3
  34. 75
  35. 42
  36. 19
  37. 6
  38. 33
  39. 3
  40. 16

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad