← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 366 · 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 two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  2. 2.The numbers 14 to 22 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) 57 (c) 162 (d) 54
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 3 (b) 5 (c) 2 (d) 4
  4. 4.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 325 (b) 288 (c) 324 (d) 315
  5. 5.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) 30 (d) 90
  6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 3 (b) 4 (c) 2 (d) 1
  7. 7.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
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 21 (b) 19 (c) 9 (d) 20
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 43? (a) 5 (b) 4 (c) 2 (d) 3
  10. 10.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 45 (c) 36 (d) 54
  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) 64 (b) 63 (c) 72 (d) 54
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 95? (a) 18 (b) 19 (c) 9 (d) 20
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 5 (b) 4 (c) 3 (d) 2
  14. 14.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  15. 15.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  16. 16.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 138 (c) 130 (d) 129
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 19 (b) 20 (c) 21 (d) 9
  19. 19.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) 23 (b) 69 (c) 72 (d) 207
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  21. 21.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) 82 (c) 64 (d) 73
  22. 22.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 6 (b) 5 (c) 8 (d) 7
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 92? (a) 9 (b) 20 (c) 19 (d) 18
  25. 25.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) 142 (c) 134 (d) 124
  26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 2 (b) 4 (c) 3 (d) 5
  27. 27.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
  28. 28.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 643 (b) 500 (c) 642 (d) 633
  29. 29.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 153 (c) 162 (d) 144
  30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 4 (b) 6 (c) 7 (d) 5
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 3 (b) 5 (c) 6 (d) 4
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 17 (b) 15 (c) 16 (d) 5
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 5 (b) 16 (c) 15 (d) 17
  34. 34.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 360 (c) 433 (d) 432
  35. 35.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  36. 36.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
  37. 37.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 42 (c) 51 (d) 60
  38. 38.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 349 (b) 348 (c) 304 (d) 339
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 2 (b) 4 (c) 5 (d) 3
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 9 (b) 5 (c) 10 (d) 7

Answer key

  1. 8
  2. 54
  3. 4
  4. 324
  5. 30
  6. 3
  7. 66
  8. 20
  9. 4
  10. 45
  11. 63
  12. 19
  13. 4
  14. 8
  15. 4
  16. 129
  17. 3
  18. 20
  19. 69
  20. 4
  21. 73
  22. 9
  23. 7
  24. 19
  25. 133
  26. 4
  27. 7
  28. 642
  29. 153
  30. 6
  31. 5
  32. 16
  33. 16
  34. 432
  35. 7
  36. 6
  37. 51
  38. 348
  39. 4
  40. 9

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