Problems(1)
Given integer n≥3. There are n dots marked 1 to n clockwise on a big circle. And between every two neighboring dots, there is a light. At first, every light were dark.
A and B are playing a game, A pick up n pairs from {(i,j)∣1≤i<j≤n} and for every pairs (i,j). B starts from the point marked i and choose to walk clockwise or counterclockwise to the point marked j. And B invert the status of all passing lights (bright ↔ dark)
A hopes the number of dark light can be as much as possible while B hopes the number of bright light can be as much as possible. Suppose A, B are both smart, how many lights are bright in the end?Proposed by BlessingOfHeavenhttps://pbs.twimg.com/profile_images/1014932415201120256/u9KAaMZ4_400x400.jpg combinatoricsgameIMOC