← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 389 · 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 7 written when you write all the numbers from 1 to 76? (a) 14 (b) 12 (c) 15 (d) 7
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 44? (a) 4 (b) 2 (c) 3 (d) 5
  3. 3.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) 60 (b) 57 (c) 19 (d) 171
  4. 4.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 505 (c) 504 (d) 495
  5. 5.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 366 (c) 432 (d) 442
  6. 6.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 127 (c) 136 (d) 128
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 3 (b) 15 (c) 13 (d) 14
  8. 8.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
  9. 9.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  10. 10.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 19 (b) 20 (c) 8 (d) 18
  12. 12.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
  13. 13.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 355 (b) 354 (c) 345 (d) 308
  14. 14.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 146 (c) 154 (d) 145
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 9 (b) 18 (c) 19 (d) 20
  16. 16.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) 21 (c) 66 (d) 63
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 15 (b) 4 (c) 13 (d) 14
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 4 (b) 6 (c) 5 (d) 7
  19. 19.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) 14 (c) 45 (d) 42
  20. 20.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) 81 (b) 27 (c) 9 (d) 30
  21. 21.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 8 (d) 13
  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) 33 (b) 30 (c) 10 (d) 90
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 15 (b) 5 (c) 14 (d) 16
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 17 (b) 6 (c) 18 (d) 16
  25. 25.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 19 (b) 18 (c) 20 (d) 8
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 8 (b) 20 (c) 18 (d) 19
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 20 (b) 21 (c) 19 (d) 9
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 18 (d) 8
  30. 30.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) 11 (b) 99 (c) 36 (d) 33
  31. 31.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 549 (c) 558 (d) 559
  32. 32.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 466 (c) 592 (d) 591
  33. 33.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) 72 (b) 8 (c) 24 (d) 27
  34. 34.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  35. 35.The numbers 16 to 24 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) 60 (c) 20 (d) 180
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 17 (b) 19 (c) 18 (d) 7
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 15 (b) 13 (c) 14 (d) 4
  38. 38.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  39. 39.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) 42 (b) 39 (c) 13 (d) 117
  40. 40.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) 69 (b) 207 (c) 23 (d) 72

Answer key

  1. 14
  2. 4
  3. 57
  4. 504
  5. 441
  6. 127
  7. 14
  8. 6
  9. 2
  10. 8
  11. 19
  12. 3
  13. 354
  14. 145
  15. 19
  16. 63
  17. 14
  18. 6
  19. 42
  20. 27
  21. 7
  22. 30
  23. 15
  24. 17
  25. 4
  26. 19
  27. 19
  28. 20
  29. 18
  30. 33
  31. 558
  32. 591
  33. 24
  34. 5
  35. 60
  36. 18
  37. 14
  38. 2
  39. 39
  40. 69

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