← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 743 · 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.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) 7 (c) 21 (d) 63
  2. 2.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) 48 (d) 45
  3. 3.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 304 (c) 339 (d) 349
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 88? (a) 8 (b) 17 (c) 19 (d) 18
  5. 5.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 176 (c) 185 (d) 194
  6. 6.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 480 (c) 612 (d) 613
  7. 7.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  8. 8.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 18 (b) 6 (c) 16 (d) 17
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 8 (b) 17 (c) 19 (d) 18
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 54? (a) 5 (b) 10 (c) 11 (d) 8
  12. 12.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) 24 (b) 216 (c) 72 (d) 75
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 1 (b) 4 (c) 3 (d) 2
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 18 (d) 19
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 4 (b) 3 (c) 6 (d) 5
  16. 16.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  17. 17.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 307 (c) 306 (d) 276
  18. 18.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) 18 (c) 15 (d) 5
  19. 19.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 39 (c) 12 (d) 108
  20. 20.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) 207 (c) 69 (d) 72
  21. 21.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  22. 22.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) 90 (b) 10 (c) 30 (d) 33
  23. 23.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 205 (b) 208 (c) 195 (d) 204
  24. 24.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 396 (c) 336 (d) 397
  25. 25.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  26. 26.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) 51 (c) 48 (d) 144
  27. 27.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) 24 (b) 72 (c) 8 (d) 27
  28. 28.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 66 (c) 76 (d) 75
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 97? (a) 21 (b) 9 (c) 19 (d) 20
  30. 30.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
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 17 (d) 8
  32. 32.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 96 (c) 105 (d) 114
  33. 33.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  34. 34.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) 98 (d) 108
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 94? (a) 21 (b) 19 (c) 20 (d) 9
  36. 36.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 113 (c) 122 (d) 104
  37. 37.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 5 (b) 15 (c) 16 (d) 17
  39. 39.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 547 (c) 546 (d) 537
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 4 (b) 2 (c) 5 (d) 3

Answer key

  1. 21
  2. 45
  3. 348
  4. 18
  5. 185
  6. 612
  7. 2
  8. 7
  9. 17
  10. 18
  11. 10
  12. 72
  13. 3
  14. 19
  15. 5
  16. 4
  17. 306
  18. 15
  19. 36
  20. 69
  21. 9
  22. 30
  23. 204
  24. 396
  25. 7
  26. 48
  27. 24
  28. 75
  29. 20
  30. 42
  31. 18
  32. 105
  33. 9
  34. 107
  35. 20
  36. 113
  37. 8
  38. 16
  39. 546
  40. 4

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