← Pigeonhole and worst case lesson New set →

Pigeonhole Principle Worksheet for Maths Olympiad

Maths Olympiad topic 23: Pigeonhole and worst case · Set 632 · 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 12 green balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 13 (b) 21 (c) 14 (d) 2
  2. 2.A bag has 11 black balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 18 (c) 12 (d) 13
  3. 3.A bag has 9 white balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 18 (b) 11 (c) 10 (d) 2
  4. 4.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
  5. 5.A bag has 8 green 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) 2 (b) 13 (c) 20 (d) 9
  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 day of the week? (a) 15 (b) 7 (c) 14 (d) 8
  7. 7.A drawer has lots of blue 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) 3 (b) 5 (c) 4 (d) 2
  8. 8.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) 13 (b) 12 (c) 25 (d) 24
  9. 9.A bag has 5 red balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 2 (c) 6 (d) 13
  10. 10.A bag has 12 green balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 18 (c) 13 (d) 14
  11. 11.A drawer has lots of yellow, red, green, white and black 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
  12. 12.A drawer has lots of blue and black 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
  13. 13.A drawer has lots of yellow, red, white, blue and black 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) 10 (d) 5
  14. 14.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) 36 (d) 25
  15. 15.A bag has 3 red balls and 4 blue 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) 4 (c) 5 (d) 2
  16. 16.A drawer has lots of white, 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) 6 (b) 3 (c) 2 (d) 4
  17. 17.A drawer has lots of yellow, 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) 6 (b) 2 (c) 3 (d) 4
  18. 18.A drawer has lots of white, red, yellow, green and black 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) 5 (c) 6 (d) 2
  19. 19.A bag has 12 red balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 13 (b) 14 (c) 15 (d) 2
  20. 20.A drawer has lots of red, 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) 3 (b) 4 (c) 2 (d) 6
  21. 21.A bag has 7 white balls and 12 blue 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) 13 (d) 19
  22. 22.A drawer has lots of green, yellow, 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) 8 (c) 2 (d) 5
  23. 23.A bag has 9 green balls and 5 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) 14 (c) 6 (d) 2
  24. 24.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) 28 (b) 29 (c) 21 (d) 22
  25. 25.A bag has 7 yellow balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 9 (b) 8 (c) 2 (d) 13
  26. 26.A drawer has lots of red, white, yellow 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) 8 (d) 4
  27. 27.A drawer has lots of blue 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) 3 (d) 4
  28. 28.A drawer has lots of red 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) 3 (b) 4 (c) 2 (d) 5
  29. 29.A drawer has lots of yellow, blue 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) 3 (b) 4 (c) 6 (d) 2
  30. 30.A bag has 5 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) 6 (b) 11 (c) 7 (d) 2
  31. 31.A bag has 5 yellow balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 2 (c) 16 (d) 12
  32. 32.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) 15 (b) 14 (c) 21 (d) 22
  33. 33.A bag has 5 green balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 6 (b) 2 (c) 7 (d) 9
  34. 34.A drawer has lots of blue 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) 3 (b) 5 (c) 4 (d) 2
  35. 35.A drawer has lots of black, yellow, 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) 8 (b) 4 (c) 5 (d) 2
  36. 36.A bag has 3 green balls and 6 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) 4 (d) 7
  37. 37.A bag has 8 yellow balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 18 (b) 10 (c) 9 (d) 2
  38. 38.A drawer has lots of blue, green, white and black 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
  39. 39.A bag has 8 green balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 10 (c) 9 (d) 11
  40. 40.A bag has 12 green 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) 2 (b) 13 (c) 18 (d) 7

Answer key

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

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