← Pigeonhole and worst case lesson New set →

Pigeonhole Principle Worksheet for Maths Olympiad

Maths Olympiad topic 23: Pigeonhole and worst case · Set 104 · 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 bag has 8 yellow balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 11 (b) 9 (c) 10 (d) 2
  2. 2.A drawer has lots of black 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) 2 (d) 4
  3. 3.A bag has 12 yellow balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 17 (b) 13 (c) 14 (d) 2
  4. 4.A bag has 4 white balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 5 (b) 2 (c) 6 (d) 15
  5. 5.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) 14 (b) 22 (c) 15 (d) 21
  6. 6.A bag has 4 green balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 2 (c) 9 (d) 5
  7. 7.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) 4 (c) 3 (d) 2
  8. 8.A bag has 6 yellow balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 9 (c) 8 (d) 7
  9. 9.A bag has 5 white 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) 2 (b) 4 (c) 8 (d) 6
  10. 10.A bag has 6 red balls and 8 white 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) 14 (c) 2 (d) 7
  11. 11.A bag has 7 red balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 2 (c) 19 (d) 8
  12. 12.A bag has 10 red balls and 12 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 22 (b) 11 (c) 2 (d) 12
  13. 13.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) 4 (b) 3 (c) 5 (d) 2
  14. 14.A bag has 3 white balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 2 (c) 7 (d) 4
  15. 15.A drawer has lots of white, yellow, red, 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) 10 (b) 2 (c) 6 (d) 5
  16. 16.A bag has 5 yellow balls and 7 green 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) 8 (d) 6
  17. 17.A bag has 6 blue balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 18 (b) 2 (c) 7 (d) 13
  18. 18.A bag has 12 black balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 13 (b) 19 (c) 2 (d) 14
  19. 19.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) 24 (b) 37 (c) 25 (d) 36
  20. 20.A bag has 7 yellow balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 8 (b) 9 (c) 2 (d) 14
  21. 21.A bag has 12 white balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 14 (c) 13 (d) 24
  22. 22.A bag has 11 white balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 18 (b) 8 (c) 12 (d) 2
  23. 23.A drawer has lots of green 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) 3 (c) 2 (d) 4
  24. 24.A bag has 10 black balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 12 (b) 2 (c) 11 (d) 13
  25. 25.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) 14 (b) 7 (c) 15 (d) 8
  26. 26.A bag has 4 green balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 6 (b) 12 (c) 5 (d) 2
  27. 27.A bag has 11 blue balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 6 (c) 2 (d) 16
  28. 28.A bag has 5 white balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 14 (b) 6 (c) 7 (d) 2
  29. 29.A bag has 6 red balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 17 (b) 8 (c) 2 (d) 7
  30. 30.A drawer has lots of yellow, blue, white, 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) 5 (b) 2 (c) 6 (d) 10
  31. 31.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 29 (b) 22 (c) 28 (d) 21
  32. 32.A drawer has lots of green, black, white 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) 2 (b) 4 (c) 8 (d) 5
  33. 33.A bag has 8 yellow balls and 7 red 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) 15 (c) 8 (d) 9
  34. 34.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) 24 (c) 13 (d) 12
  35. 35.A bag has 4 black balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 5 (b) 6 (c) 2 (d) 9
  36. 36.A bag has 5 white balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 7 (b) 16 (c) 6 (d) 2
  37. 37.A drawer has lots of black, blue, 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) 2 (b) 5 (c) 6 (d) 10
  38. 38.A drawer has lots of red, blue, black, green 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) 2 (b) 5 (c) 10 (d) 6
  39. 39.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 37 (b) 36 (c) 48 (d) 49
  40. 40.A drawer has lots of blue, white, 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) 2 (b) 5 (c) 6 (d) 10

Answer key

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

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