← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 739 · 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 2 written when you write all the numbers from 1 to 81? (a) 8 (b) 18 (c) 17 (d) 19
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 4 (b) 5 (c) 3 (d) 2
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 18 (b) 17 (c) 8 (d) 19
  4. 4.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 394 (c) 474 (d) 484
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 9 (b) 21 (c) 19 (d) 20
  6. 6.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) 54 (c) 6 (d) 21
  7. 7.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 228 (c) 238 (d) 230
  8. 8.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 12 (d) 8
  9. 9.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) 21 (b) 63 (c) 24 (d) 7
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 15 (b) 6 (c) 16 (d) 17
  12. 12.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 488 (b) 625 (c) 615 (d) 624
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 2 (b) 3 (c) 4 (d) 1
  14. 14.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) 24 (c) 216 (d) 75
  15. 15.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 133 (b) 134 (c) 142 (d) 124
  16. 16.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 505 (c) 495 (d) 408
  17. 17.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) 69 (b) 66 (c) 22 (d) 198
  18. 18.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 85 (c) 94 (d) 76
  19. 19.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 18 (b) 9 (c) 19 (d) 20
  21. 21.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 394 (c) 393 (d) 334
  22. 22.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) 27 (b) 30 (c) 9 (d) 81
  23. 23.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
  24. 24.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  25. 25.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) 11 (d) 33
  26. 26.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 4 (d) 10
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 2 (b) 4 (c) 3 (d) 5
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 5 (b) 2 (c) 4 (d) 3
  29. 29.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) 13 (b) 117 (c) 42 (d) 39
  30. 30.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 7 (d) 14
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 1 (b) 2 (c) 3 (d) 4
  32. 32.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 156 (c) 146 (d) 155
  33. 33.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) 15 (b) 5 (c) 18 (d) 45
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 60? (a) 5 (b) 8 (c) 7 (d) 6
  35. 35.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  36. 36.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 128 (c) 137 (d) 146
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 6 (b) 17 (c) 18 (d) 16
  38. 38.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 100 (c) 91 (d) 82
  39. 39.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 13 (b) 14 (c) 12 (d) 3

Answer key

  1. 18
  2. 4
  3. 18
  4. 483
  5. 20
  6. 18
  7. 237
  8. 8
  9. 21
  10. 2
  11. 16
  12. 624
  13. 3
  14. 72
  15. 133
  16. 504
  17. 66
  18. 85
  19. 5
  20. 19
  21. 393
  22. 27
  23. 45
  24. 8
  25. 33
  26. 3
  27. 4
  28. 4
  29. 39
  30. 6
  31. 3
  32. 155
  33. 15
  34. 7
  35. 7
  36. 137
  37. 17
  38. 91
  39. 4
  40. 13

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