← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 227 · 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 9 written when you write all the numbers from 1 to 57? (a) 4 (b) 5 (c) 3 (d) 6
  2. 2.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) 48 (c) 144 (d) 51
  3. 3.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) 54 (b) 51 (c) 17 (d) 153
  4. 4.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 77 (b) 86 (c) 78 (d) 68
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 3 (b) 2 (c) 4 (d) 5
  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) 72 (b) 23 (c) 69 (d) 207
  7. 7.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) 135 (b) 15 (c) 45 (d) 48
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
  9. 9.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16
  10. 10.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  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) 18 (b) 5 (c) 45 (d) 15
  12. 12.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 416 (c) 517 (d) 516
  13. 13.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) 18 (b) 6 (c) 54 (d) 21
  14. 14.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 459 (c) 460 (d) 450
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 17 (b) 5 (c) 16 (d) 15
  16. 16.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  18. 18.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) 30 (b) 33 (c) 90 (d) 10
  19. 19.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) 27 (b) 72 (c) 8 (d) 24
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 8 (b) 20 (c) 18 (d) 19
  21. 21.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) 36 (c) 33 (d) 11
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 3 (b) 5 (c) 4 (d) 2
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 4 (b) 2 (c) 3 (d) 5
  24. 24.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 6 (b) 7 (c) 5 (d) 8
  26. 26.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 107 (b) 116 (c) 108 (d) 98
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 8 (b) 20 (c) 18 (d) 19
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 13 (b) 3 (c) 14 (d) 15
  29. 29.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 158 (c) 148 (d) 157
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 6 (b) 18 (c) 16 (d) 17
  31. 31.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) 19 (b) 57 (c) 60 (d) 171
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 9 (b) 6 (c) 8 (d) 7
  33. 33.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  34. 34.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) 75 (b) 24 (c) 216 (d) 72
  35. 35.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) 116 (c) 115 (d) 124
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 9 (b) 8 (c) 7 (d) 6
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 18 (b) 17 (c) 19 (d) 8
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 15 (b) 17 (c) 5 (d) 16
  39. 39.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) 63 (b) 66 (c) 189 (d) 21
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 15 (b) 17 (c) 5 (d) 16

Answer key

  1. 5
  2. 48
  3. 51
  4. 77
  5. 4
  6. 69
  7. 45
  8. 5
  9. 4
  10. 9
  11. 15
  12. 516
  13. 18
  14. 459
  15. 16
  16. 8
  17. 3
  18. 30
  19. 24
  20. 19
  21. 33
  22. 4
  23. 4
  24. 6
  25. 7
  26. 107
  27. 19
  28. 14
  29. 157
  30. 17
  31. 57
  32. 8
  33. 7
  34. 72
  35. 115
  36. 8
  37. 18
  38. 16
  39. 63
  40. 16

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