← Pigeonhole and worst case lesson New set →

Pigeonhole Principle Worksheet for Maths Olympiad

Maths Olympiad topic 23: Pigeonhole and worst case · Set 666 · 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 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) 4 (d) 3
  2. 2.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) 2 (b) 3 (c) 4 (d) 5
  3. 3.A bag has 6 black balls and 11 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) 12 (c) 2 (d) 17
  4. 4.A drawer has lots of green, 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) 3 (c) 6 (d) 4
  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) 21 (d) 15
  6. 6.A bag has 5 green 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) 2 (b) 12 (c) 6 (d) 16
  7. 7.A bag has 7 black balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 9 (b) 18 (c) 8 (d) 2
  8. 8.A bag has 5 blue balls and 7 white 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) 6 (c) 2 (d) 12
  9. 9.A drawer has lots of blue, black 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) 3 (c) 2 (d) 4
  10. 10.A drawer has lots of green 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) 5 (d) 2
  11. 11.A bag has 9 yellow balls and 10 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 19 (b) 2 (c) 10 (d) 11
  12. 12.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) 36 (b) 48 (c) 49 (d) 37
  13. 13.A bag has 7 green balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 18 (b) 9 (c) 8 (d) 2
  14. 14.A bag has 5 white balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 13 (c) 6 (d) 7
  15. 15.A bag has 3 blue balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 5 (c) 10 (d) 4
  16. 16.A bag has 6 blue balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 7 (b) 2 (c) 13 (d) 8
  17. 17.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
  18. 18.A bag has 7 white balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 9 (c) 8 (d) 13
  19. 19.A drawer has lots of yellow, white, red, 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) 5 (b) 10 (c) 6 (d) 2
  20. 20.A bag has 9 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) 2 (b) 10 (c) 14 (d) 6
  21. 21.A bag has 11 yellow balls and 9 white 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) 20 (c) 10 (d) 12
  22. 22.A bag has 10 blue balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 12 (c) 17 (d) 11
  23. 23.A drawer has lots of 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) 4 (b) 3 (c) 5 (d) 2
  24. 24.A drawer has lots of 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) 3 (b) 2 (c) 5 (d) 4
  25. 25.A drawer has lots of yellow, white, green, red 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) 2 (d) 6
  26. 26.A drawer has lots of black 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) 5 (c) 2 (d) 3
  27. 27.A bag has 3 white balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 10 (c) 5 (d) 4
  28. 28.A bag has 10 black balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 22 (b) 11 (c) 12 (d) 2
  29. 29.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) 8 (c) 14 (d) 7
  30. 30.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) 24 (c) 37 (d) 25
  31. 31.A bag has 4 white balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 6 (b) 5 (c) 2 (d) 15
  32. 32.A drawer has lots of yellow, 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) 4 (c) 2 (d) 3
  33. 33.A bag has 8 green balls and 3 blue 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) 2 (c) 11 (d) 9
  34. 34.A bag has 4 blue balls and 10 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) 11 (c) 14 (d) 2
  35. 35.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) 10 (c) 6 (d) 5
  36. 36.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) 4 (b) 3 (c) 2 (d) 5
  37. 37.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) 8 (b) 4 (c) 5 (d) 2
  38. 38.A bag has 9 black balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 20 (b) 2 (c) 10 (d) 12
  39. 39.A bag has 11 green balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 13 (b) 14 (c) 2 (d) 12
  40. 40.A bag has 6 blue balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 8 (b) 7 (c) 2 (d) 11

Answer key

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

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