HMMT 十一月 2011 · THM 赛 · 第 1 题
HMMT November 2011 — THM Round — Problem 1
题目详情
- [ 3 ] Five of James’ friends are sitting around a circular table to play a game of Fish. James chooses aplace between two of his friends to pull up a chair and sit. Then, the six friends divide themselves intotwo disjoint teams, with each team consisting of three consecutive players at the table. If the order inwhich the three members of a team sit does not matter, how many possible (unordered) pairs of teamsare possible?
英文原题
He gives a card to a random player.
解析
英文解析
- [ 3 ] Five of James’ friends are sitting around a circular table to play a game of Fish. James chooses aplace between two of his friends to pull up a chair and sit. Then, the six friends divide themselves intotwo disjoint teams, with each team consisting of three consecutive players at the table. If the order inwhich the three members of a team sit does not matter, how many possible (unordered) pairs of teamsare possible?
Answer: 5 Note that the team not containing James must consist of three consecutive players whoare already seated. We have 5 choices for the player sitting furthest clockwise on the team of which
James is not a part. The choice of this player uniquely determines the teams, so we have a total of 5
possible pairs.