← Pigeonhole and worst case lesson New set →

Pigeonhole Principle Worksheet for Maths Olympiad

Maths Olympiad topic 23: Pigeonhole and worst case · Set 190 · 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 three of them were born in the same day of the week? (a) 14 (b) 21 (c) 15 (d) 22
  2. 2.A bag has 9 green 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) 13 (b) 5 (c) 10 (d) 2
  3. 3.A bag has 3 red balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 12 (b) 5 (c) 2 (d) 4
  4. 4.A bag has 6 white balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 7 (c) 8 (d) 14
  5. 5.A bag has 12 yellow balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 13 (b) 2 (c) 22 (d) 14
  6. 6.A drawer has lots of green, white 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) 4 (c) 2 (d) 3
  7. 7.A bag has 3 green balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 4 (c) 5 (d) 13
  8. 8.A drawer has lots of red, black, white, 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) 6 (b) 10 (c) 2 (d) 5
  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 day of the week? (a) 7 (b) 14 (c) 8 (d) 15
  10. 10.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) 3 (b) 4 (c) 5 (d) 2
  11. 11.A bag has 3 blue balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 11 (b) 4 (c) 2 (d) 5
  12. 12.A drawer has lots of red, white, black, 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) 2 (b) 10 (c) 6 (d) 5
  13. 13.A drawer has lots of yellow, 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) 4 (d) 2
  14. 14.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) 13 (c) 24 (d) 12
  15. 15.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) 2 (b) 4 (c) 3 (d) 5
  16. 16.A drawer has lots of black, yellow, 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) 2 (b) 5 (c) 8 (d) 4
  17. 17.A bag has 10 white balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 12 (b) 19 (c) 11 (d) 2
  18. 18.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) 28 (c) 22 (d) 21
  19. 19.A drawer has lots of green, yellow, 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) 5 (b) 6 (c) 10 (d) 2
  20. 20.A bag has 9 green balls and 4 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) 10 (c) 5 (d) 13
  21. 21.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) 4 (b) 3 (c) 6 (d) 2
  22. 22.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) 5 (b) 3 (c) 4 (d) 2
  23. 23.A bag has 5 black 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) 14 (b) 6 (c) 10 (d) 2
  24. 24.A drawer has lots of blue, red, 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) 4 (c) 8 (d) 5
  25. 25.A drawer has lots of white 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) 4 (b) 3 (c) 5 (d) 2
  26. 26.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) 48 (b) 49 (c) 36 (d) 37
  27. 27.A bag has 10 white 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) 11 (b) 7 (c) 16 (d) 2
  28. 28.A bag has 9 white balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 11 (b) 12 (c) 10 (d) 2
  29. 29.A bag has 8 white balls and 3 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) 4 (c) 9 (d) 11
  30. 30.A drawer has lots of green, 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) 3 (c) 6 (d) 4
  31. 31.A bag has 10 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) 11 (b) 19 (c) 2 (d) 10
  32. 32.A drawer has lots of blue, red, 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) 5 (b) 10 (c) 6 (d) 2
  33. 33.A bag has 8 white balls and 6 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) 7 (c) 14 (d) 9
  34. 34.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) 4 (b) 3 (c) 5 (d) 2
  35. 35.A bag has 6 red balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 8 (b) 2 (c) 7 (d) 9
  36. 36.A bag has 5 white 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) 11 (b) 6 (c) 15 (d) 2
  37. 37.A bag has 6 red balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 10 (b) 2 (c) 7 (d) 8
  38. 38.A bag has 4 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) 2 (b) 5 (c) 10 (d) 7
  39. 39.A drawer has lots of red, 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) 3 (b) 2 (c) 4 (d) 6
  40. 40.A drawer has lots of red, green, yellow, 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) 2 (c) 10 (d) 6

Answer key

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

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