镜厅
Hall of Mirrors
题目详情
Alongside the grid above there are several arrows. Red arrows indicate a laser being shone in the given direction, from just off the edge of the grid. Blue arrows indicate a goal. Your job is to add diagonal mirrors to the grid so that as many lasers reach their goal as possible. A mirror cuts across one or more cells at a 45-degree angle (a cell can contain at most one mirror).
You receive 5 points for every incoming laser that gets redirected to a goal, and you lose (N+2) points for every mirror you install, where N is the length of the mirror. (Mirrors may cross over each other. E.g. you could have an “X” shape using two length-2 mirrors, which would count as two length-2 mirrors and not as one length-4 mirror.)
What’s the highest score you can achieve?
解析
Original Explanation
In this month’s puzzle it was hard to know for sure if you had an optimal solution, but there were a few things to note:
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There were more laser entrances (24) than exits (21), so not every laser can reach a target.
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You get more points for a successful laser than you lose for a wall of length 1, so in general building mirrors is worthwhile, even if they’re small.
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There were some locations where placing one mirror caused 2 lasers on opposite ends to reach their goals.
The best solution we received (and the best we’re aware of) totalled 77 points. It is shone above. Congratulations to Sébastien Geeraert, this month’s high-scorer and winner of a Jane Street t-shirt!