← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 601 · 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) 7 (c) 8 (d) 10
  2. 2.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) 66 (b) 189 (c) 21 (d) 63
  3. 3.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) 15 (b) 135 (c) 45 (d) 48
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 20 (b) 9 (c) 19 (d) 21
  5. 5.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) 27 (c) 72 (d) 8
  6. 6.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) 194 (d) 185
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 7 (b) 18 (c) 17 (d) 19
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  9. 9.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  10. 10.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 4 (b) 3 (c) 5 (d) 2
  12. 12.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 570 (c) 580 (d) 579
  13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 3 (b) 4 (c) 6 (d) 5
  14. 14.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) 42 (c) 14 (d) 126
  15. 15.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 272 (c) 300 (d) 291
  16. 16.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) 54 (b) 6 (c) 18 (d) 21
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 4 (b) 15 (c) 14 (d) 13
  18. 18.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  20. 20.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
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 3 (b) 1 (c) 4 (d) 2
  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) 90 (c) 10 (d) 30
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 3 (d) 4
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 16 (b) 8 (c) 13 (d) 15
  25. 25.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 385 (c) 375 (d) 384
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 20 (b) 9 (c) 19 (d) 21
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 18 (b) 19 (c) 16 (d) 9
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 19 (b) 8 (c) 18 (d) 20
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 15 (b) 13 (c) 14 (d) 3
  30. 30.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) 117 (b) 42 (c) 39 (d) 13
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 5 (b) 3 (c) 4 (d) 2
  32. 32.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3
  33. 33.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 466 (c) 456 (d) 465
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 17 (b) 16 (c) 6 (d) 15
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 18 (b) 17 (c) 16 (d) 6
  36. 36.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) 5 (c) 15 (d) 18
  37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 18 (b) 16 (c) 17 (d) 6
  38. 38.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 156 (c) 164 (d) 155
  39. 39.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 74 (c) 65 (d) 66
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 4 (b) 3 (c) 6 (d) 5

Answer key

  1. 8
  2. 63
  3. 45
  4. 20
  5. 24
  6. 185
  7. 18
  8. 5
  9. 4
  10. 7
  11. 4
  12. 579
  13. 5
  14. 42
  15. 300
  16. 18
  17. 14
  18. 6
  19. 3
  20. 57
  21. 3
  22. 30
  23. 3
  24. 15
  25. 384
  26. 20
  27. 18
  28. 19
  29. 14
  30. 39
  31. 4
  32. 3
  33. 465
  34. 16
  35. 17
  36. 15
  37. 17
  38. 155
  39. 65
  40. 5

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