Related to open problem #1: Don't fight each other
Logic
Level
2
What is the maximum number of bishops you can place on this chessboard such that none of them can attack each other in one move?
7
8
4
5
6
9
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1 solution
8 bishops is maximum.
We have shown that 8 can be archived. Now we are going to show why we can't place 9 or more bishops.
A bishop move like this:
Meaning that it can only attack in this way.
We will not place any bishops at a5 to e5 and a1 to e1. Here is a possibility:
Which is only 5 bishops.
Now, we will place bishops at center, up and down. Note that if we place bishops at center, we cannot place it at corner. Here is a possibility:
Which is only 7 bishops.
Now, we will place bishops at corner, up and down. Here is a possibility:
Which is only 6 bishops. Now, we have only one strong choice. Which is to place the bishops at only at upside and downside.