← Pigeonhole and worst case lesson New set →

Pigeonhole Principle Worksheet for Maths Olympiad

Maths Olympiad topic 23: Pigeonhole and worst case · Set 366 · 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, 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) 3 (b) 2 (c) 6 (d) 4
  2. 2.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) 25 (c) 36 (d) 37
  3. 3.A bag has 11 red balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 19 (b) 2 (c) 9 (d) 12
  4. 4.A drawer has lots of green, black, 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) 2 (b) 5 (c) 8 (d) 4
  5. 5.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) 49 (b) 36 (c) 48 (d) 37
  6. 6.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
  7. 7.A bag has 8 black 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) 15 (c) 9 (d) 10
  8. 8.A drawer has lots of green, yellow, 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) 4 (c) 2 (d) 8
  9. 9.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) 24 (c) 12 (d) 25
  10. 10.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) 4 (b) 3 (c) 6 (d) 2
  11. 11.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) 5 (b) 3 (c) 2 (d) 4
  12. 12.A drawer has lots of red, green, 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) 2 (b) 10 (c) 6 (d) 5
  13. 13.A drawer has lots of green, yellow, white, 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) 6 (b) 5 (c) 2 (d) 10
  14. 14.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) 21 (b) 29 (c) 28 (d) 22
  15. 15.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) 15 (c) 14 (d) 8
  16. 16.A bag has 10 red balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 16 (b) 12 (c) 2 (d) 11
  17. 17.A bag has 7 blue balls and 9 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) 16 (c) 8 (d) 10
  18. 18.A drawer has lots of red, white, 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) 5 (b) 2 (c) 8 (d) 4
  19. 19.A bag has 10 red 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) 5 (c) 11 (d) 14
  20. 20.A bag has 11 green balls and 9 black 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) 20 (d) 12
  21. 21.A drawer has lots of red, green, blue, 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) 2 (b) 6 (c) 5 (d) 10
  22. 22.A drawer has lots of green, red, 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) 8 (b) 4 (c) 5 (d) 2
  23. 23.A bag has 10 black balls and 5 blue 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) 11 (c) 2 (d) 6
  24. 24.A drawer has lots of red, yellow 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) 2 (b) 4 (c) 6 (d) 3
  25. 25.A bag has 10 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) 2 (b) 11 (c) 22 (d) 13
  26. 26.A bag has 12 blue balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 13 (b) 16 (c) 14 (d) 2
  27. 27.A bag has 12 white balls and 9 blue 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) 10 (c) 21 (d) 2
  28. 28.A bag has 5 red balls and 12 white 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) 13 (c) 2 (d) 6
  29. 29.A bag has 9 red balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 11 (b) 19 (c) 10 (d) 2
  30. 30.A drawer has lots of blue, white, 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) 5 (b) 8 (c) 2 (d) 4
  31. 31.A bag has 6 red balls and 7 yellow 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) 7 (c) 13 (d) 2
  32. 32.A drawer has lots of yellow 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) 2 (b) 4 (c) 3 (d) 5
  33. 33.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) 4 (b) 5 (c) 2 (d) 3
  34. 34.A drawer has lots of yellow, 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) 3 (b) 2 (c) 4 (d) 6
  35. 35.A drawer has lots of blue, white, yellow 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) 8 (b) 5 (c) 2 (d) 4
  36. 36.A bag has 9 green balls and 12 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) 13 (c) 21 (d) 2
  37. 37.A drawer has lots of 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) 4 (b) 2 (c) 5 (d) 3
  38. 38.A drawer has lots of 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) 2 (b) 5 (c) 4 (d) 3
  39. 39.A bag has 7 white balls and 5 black 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) 8 (c) 2 (d) 12
  40. 40.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) 4 (d) 3

Answer key

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

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