双人舞
Pair Dance
题目详情
15 dancers are standing in an equilateral triangle formation, with every dancer standing 1 unit apart from her nearest neighbors. Each dancer chooses another who is 1 unit away to pair up with, and all but 1 dancer ends up as a part of a pair. An example of one such arrangement is presented here.
How many different sets of 7 pairs are possible?
解析
有 240 种可能的组合，每组 7 对。计数可能会有点棘手，但是 按未配对的舞者类型进行分类，然后减少 对称性是一个很好的起点。
祝贺所有正确解决问题的人，特别是 Shahmeer Navid， 本月随机选出的 Jane Street T 恤获奖者！
Original Explanation
There are 240 possible sets of 7 pairs. The counting can get a bit tricky, but categorizing by which type of dancer remains un-paired, and then reducing by symmetry is a good place to start.
Congratulations to all of those who solved correctly, especially Shahmeer Navid, this month’s randomly-chosen winner of a Jane Street t-shirt!