← Pigeonhole and worst case lesson New set →

Pigeonhole Principle Worksheet for Maths Olympiad

Maths Olympiad topic 23: Pigeonhole and worst case · Set 69 · 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.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) 25 (c) 12 (d) 24
  2. 2.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
  3. 3.A bag has 5 green balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 6 (b) 15 (c) 2 (d) 7
  4. 4.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) 6 (c) 2 (d) 4
  5. 5.A bag has 7 white 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) 4 (b) 2 (c) 10 (d) 8
  6. 6.A drawer has lots of 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) 6 (b) 3 (c) 2 (d) 4
  7. 7.A bag has 11 red balls and 6 blue 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) 7 (c) 12 (d) 2
  8. 8.A bag has 8 green balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 9 (b) 16 (c) 2 (d) 10
  9. 9.A bag has 7 yellow 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) 2 (b) 12 (c) 18 (d) 8
  10. 10.A drawer has lots of yellow, 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) 4 (b) 3 (c) 2 (d) 6
  11. 11.A bag has 11 yellow balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 13 (c) 12 (d) 14
  12. 12.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) 15 (c) 21 (d) 14
  13. 13.A bag has 7 white 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) 16 (b) 2 (c) 8 (d) 10
  14. 14.A drawer has lots of 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) 5 (b) 3 (c) 4 (d) 2
  15. 15.A bag has 7 white balls and 8 black 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) 9 (c) 8 (d) 2
  16. 16.A bag has 5 black balls and 10 blue 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) 11 (d) 6
  17. 17.A bag has 5 yellow balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 10 (b) 6 (c) 2 (d) 7
  18. 18.A bag has 11 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) 12 (b) 2 (c) 16 (d) 6
  19. 19.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) 5 (b) 2 (c) 3 (d) 4
  20. 20.A drawer has lots of yellow, red, blue, 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) 2 (c) 6 (d) 10
  21. 21.A bag has 3 green 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) 10 (b) 12 (c) 4 (d) 2
  22. 22.A bag has 12 red balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 13 (b) 2 (c) 14 (d) 19
  23. 23.A bag has 4 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) 9 (b) 5 (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 month? (a) 36 (b) 37 (c) 49 (d) 48
  25. 25.A bag has 8 blue balls and 10 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) 18 (c) 9 (d) 11
  26. 26.A drawer has lots of green, black 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) 6 (c) 4 (d) 2
  27. 27.A drawer has lots of green, 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) 2 (b) 4 (c) 3 (d) 6
  28. 28.A drawer has lots of blue, black, 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) 2 (c) 6 (d) 10
  29. 29.A drawer has lots of yellow, 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) 6 (c) 4 (d) 2
  30. 30.A bag has 7 white balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 9 (b) 8 (c) 2 (d) 10
  31. 31.A drawer has lots of 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) 6 (b) 4 (c) 3 (d) 2
  32. 32.A drawer has lots of red, blue, green, 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) 10 (b) 2 (c) 6 (d) 5
  33. 33.A bag has 3 blue 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) 4 (b) 10 (c) 2 (d) 8
  34. 34.A bag has 12 red balls and 13 white 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) 13 (c) 25 (d) 2
  35. 35.A drawer has lots of black, 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) 8 (b) 2 (c) 5 (d) 4
  36. 36.A bag has 9 red balls and 8 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) 10 (c) 9 (d) 17
  37. 37.A bag has 8 yellow 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) 14 (b) 2 (c) 9 (d) 7
  38. 38.A bag has 9 yellow balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 11 (c) 21 (d) 10
  39. 39.A bag has 9 yellow balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 11 (b) 16 (c) 2 (d) 10
  40. 40.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) 21 (d) 28

Answer key

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

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