← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 75 · 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 7? (a) 8 (b) 6 (c) 10 (d) 7
  2. 2.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 67 (c) 58 (d) 76
  3. 3.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) 21 (d) 66
  4. 4.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) 45 (c) 15 (d) 5
  5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 4 (b) 14 (c) 15 (d) 13
  6. 6.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 53 (b) 54 (c) 44 (d) 62
  7. 7.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) 126 (b) 42 (c) 45 (d) 14
  8. 8.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) 27 (c) 24 (d) 72
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 19 (b) 18 (c) 20 (d) 9
  10. 10.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 63? (a) 11 (b) 6 (c) 8 (d) 10
  12. 12.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) 24 (b) 63 (c) 7 (d) 21
  13. 13.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 363 (c) 354 (d) 314
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 5 (b) 7 (c) 6 (d) 4
  15. 15.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) 21 (c) 54 (d) 18
  16. 16.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 187 (b) 178 (c) 196 (d) 188
  17. 17.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 68 (c) 60 (d) 59
  18. 18.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 580 (b) 458 (c) 570 (d) 579
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 19 (b) 18 (c) 8 (d) 17
  20. 20.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) 33 (d) 36
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 1 (b) 3 (c) 2 (d) 4
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 9 (b) 20 (c) 21 (d) 19
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 14 (b) 16 (c) 15 (d) 4
  25. 25.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 224 (b) 229 (c) 219 (d) 228
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 15 (b) 14 (c) 13 (d) 3
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 9 (b) 19 (c) 20 (d) 21
  28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 3 (b) 13 (c) 12 (d) 11
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 6 (b) 5 (c) 3 (d) 4
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 99? (a) 20 (b) 19 (c) 21 (d) 9
  31. 31.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 186 (c) 178 (d) 177
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 4 (b) 2 (c) 5 (d) 3
  33. 33.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 392 (b) 480 (c) 471 (d) 481
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 16 (d) 5
  35. 35.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 26 (c) 44 (d) 35
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 7 (b) 17 (c) 18 (d) 19
  37. 37.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  38. 38.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 448 (c) 447 (d) 438
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 19 (b) 21 (c) 9 (d) 20
  40. 40.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3

Answer key

  1. 7
  2. 67
  3. 63
  4. 15
  5. 14
  6. 53
  7. 42
  8. 24
  9. 19
  10. 9
  11. 10
  12. 21
  13. 363
  14. 6
  15. 18
  16. 187
  17. 59
  18. 579
  19. 18
  20. 33
  21. 3
  22. 20
  23. 3
  24. 15
  25. 228
  26. 14
  27. 20
  28. 12
  29. 5
  30. 20
  31. 177
  32. 4
  33. 480
  34. 16
  35. 35
  36. 18
  37. 6
  38. 447
  39. 20
  40. 4

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