← Pigeonhole and worst case lesson New set →

Pigeonhole Principle Worksheet for Maths Olympiad

Maths Olympiad topic 23: Pigeonhole and worst case · Set 960 · 40 questions
TalentJR

How to solve it (Think of the unluckiest case): Imagine the unluckiest draws: how many can you take and still NOT have what you want? Add 1 to that number — the next one must give it. Pigeonhole: with n boxes (colours, months, days), n × (k − 1) + 1 things make sure some box has at least k.

NameDateTime takenScore ___ / 40
  1. 1.A drawer has lots of black, green and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 3 (c) 2 (d) 6
  2. 2.A bag has 6 green balls and 12 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 18 (b) 2 (c) 8 (d) 7
  3. 3.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 22 (b) 21 (c) 14 (d) 15
  4. 4.A bag has 4 white balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 14 (c) 6 (d) 5
  5. 5.A bag has 10 green balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 11 (c) 4 (d) 13
  6. 6.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 12 (c) 24 (d) 13
  7. 7.A bag has 3 red balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 5 (c) 2 (d) 4
  8. 8.A drawer has lots of black, blue, red and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 2 (c) 5 (d) 4
  9. 9.A bag has 8 white balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 19 (d) 12
  10. 10.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 14 (c) 15 (d) 8
  11. 11.A bag has 5 black balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 7 (b) 6 (c) 2 (d) 15
  12. 12.A bag has 10 blue balls and 5 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 15 (b) 2 (c) 11 (d) 12
  13. 13.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 37 (c) 24 (d) 25
  14. 14.A bag has 9 blue balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 2 (c) 10 (d) 7
  15. 15.A bag has 3 blue balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 5 (c) 4 (d) 10
  16. 16.A bag has 9 green balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 2 (c) 11 (d) 19
  17. 17.A bag has 12 black balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 13 (c) 14 (d) 22
  18. 18.A bag has 9 green balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 11 (c) 13 (d) 10
  19. 19.A drawer has lots of black and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 5 (c) 3 (d) 4
  20. 20.A drawer has lots of red, green, yellow and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 2 (c) 8 (d) 5
  21. 21.A drawer has lots of red and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 2 (c) 3 (d) 4
  22. 22.A bag has 6 yellow balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 11 (b) 8 (c) 7 (d) 2
  23. 23.A bag has 4 blue balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 7 (c) 5 (d) 2
  24. 24.A bag has 3 red balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 6 (b) 5 (c) 2 (d) 4
  25. 25.A bag has 7 black balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 2 (c) 11 (d) 17
  26. 26.A drawer has lots of white and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 3 (c) 2 (d) 4
  27. 27.A drawer has lots of yellow and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 3 (c) 4 (d) 2
  28. 28.A bag has 8 white balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 10 (b) 2 (c) 17 (d) 9
  29. 29.A drawer has lots of white and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 2 (c) 3 (d) 5
  30. 30.A drawer has lots of blue and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 5 (c) 2 (d) 4
  31. 31.A drawer has lots of red, white and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 6 (c) 4 (d) 2
  32. 32.A drawer has lots of red and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 2 (c) 3 (d) 4
  33. 33.A bag has 3 red balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 8 (b) 2 (c) 4 (d) 5
  34. 34.A drawer has lots of blue, green, white, red and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 2 (c) 5 (d) 10
  35. 35.A drawer has lots of blue, black, red and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 2 (c) 4 (d) 8
  36. 36.A bag has 5 blue balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 14 (b) 2 (c) 10 (d) 6
  37. 37.A bag has 8 black balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 16 (b) 2 (c) 9 (d) 10
  38. 38.A drawer has lots of white and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 3 (c) 2 (d) 5
  39. 39.A bag has 9 green balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 15 (b) 2 (c) 10 (d) 11
  40. 40.A bag has 8 blue balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 12 (c) 5 (d) 9

Answer key

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

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