← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 695 · 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 10? (a) 10 (b) 8 (c) 11 (d) 9
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 19 (b) 18 (c) 7 (d) 17
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 14 (b) 16 (c) 5 (d) 15
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 5 (b) 4 (c) 7 (d) 6
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 20 (b) 18 (c) 8 (d) 19
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  7. 7.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) 336 (c) 396 (d) 397
  8. 8.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 153 (c) 54 (d) 17
  9. 9.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) 63 (b) 189 (c) 21 (d) 66
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 15 (b) 16 (c) 14 (d) 5
  11. 11.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 585 (c) 594 (d) 595
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 19 (d) 20
  13. 13.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  14. 14.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) 24 (c) 8 (d) 27
  15. 15.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) 72 (c) 216 (d) 75
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 15 (b) 6 (c) 17 (d) 16
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 17 (b) 7 (c) 19 (d) 18
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 95? (a) 18 (b) 9 (c) 19 (d) 20
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 9 (b) 8 (c) 3 (d) 7
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 10 (d) 6
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 92? (a) 20 (b) 9 (c) 21 (d) 19
  22. 22.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) 54 (c) 57 (d) 162
  23. 23.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 105 (c) 96 (d) 106
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 19 (d) 21
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 7 (d) 18
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 16 (b) 15 (c) 17 (d) 5
  27. 27.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 67? (a) 8 (b) 5 (c) 7 (d) 6
  29. 29.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  30. 30.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 277 (c) 256 (d) 276
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 19 (b) 20 (c) 8 (d) 18
  32. 32.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 2 (b) 4 (c) 1 (d) 3
  34. 34.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 372 (c) 450 (d) 451
  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) 180 (b) 20 (c) 63 (d) 60
  36. 36.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) 24 (c) 7 (d) 63
  37. 37.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 5 (b) 3 (c) 2 (d) 4
  39. 39.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) 108 (b) 39 (c) 36 (d) 12
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 72? (a) 6 (b) 8 (c) 7 (d) 5

Answer key

  1. 9
  2. 18
  3. 15
  4. 6
  5. 19
  6. 2
  7. 396
  8. 51
  9. 63
  10. 15
  11. 594
  12. 20
  13. 7
  14. 24
  15. 72
  16. 16
  17. 18
  18. 19
  19. 8
  20. 7
  21. 20
  22. 54
  23. 105
  24. 20
  25. 18
  26. 16
  27. 9
  28. 7
  29. 2
  30. 276
  31. 19
  32. 5
  33. 3
  34. 450
  35. 60
  36. 21
  37. 4
  38. 4
  39. 36
  40. 7

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