If Fenton pulls out 10 cups, he might have three of one type of cup, and three of another
type of cup, but he will be sure to have at least four matching cups.
The self-defined Masters of Cup Counting came up with our best solution and story-line. Thanks goes to Nicholas McNaughton, Jeremy Birch and Michael Sharp of Christ Church Grammer School in Perth, Australia for keeping us all entertained.
Poor Fenton will have to clean up his house before his three associates arrive anyway, but if he leaves his house as it is then he will have to take 10 cups out of the drawer before it is ensured that he has four matching ones.
The reasoning my group used for this is called WCS or Worst Case Scenario. The worst possible thing to happen is for Fenton to pull out three of each cup type before he pulls out another one to make a group of four. The total number of cups he needs to withdraw from the drawer (yeah, yeah) is therefore 10. Even if he gets the 10 cups out he will have a hard time telling which one is which, so he will have to get a torch anyway.
This tasty solution came from Robert House, also of Christ Church Grammer School. Robert explained the reasoning behind the solution better than our snarky mascot...
Fenton must take out 10 cups to ensure him of getting four matching cups. The very worst scenario is that every cup he takes out is different so that there is three of every cup pattern. This makes up 9 cups. The next one he takes out must match with one of these. Therefore he must take out ten cups.
Andre Asbury [firstname.lastname@example.org] was right on target with his answer:
My answer to this math challenge is that he will need to pull out ten (10) cups to ensure a match.
Simon Blackwell's group from CCGS of Western Australia have put themselves on Minus' favourite feeders list with this answer:
Our group came up with the answer that Fenton needs to take out 10 cups to find the four matching ones.