Knight Knight Sleep Tight I
What is the minimum number of knights placed on an chessboard which are needed to cover every square?
Details and Assumptions:
- The diagram above shows the squares coloured green that could be reached by a knight on the purple square, following a standard Knight's move
- " Cover " includes both the squares that each knight is standing on and the squares that each knight can attack (both purple and green in the above diagram)
This problem is part of the Knight Knight Sleep Tight set.
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1 solution
In the above image, note that no single knight can cover 2 (or more) of the green squares. Therefore, each of these green squares requires 1 knight on the board, meaning that at least 1 2 knights are needed.
In the above image, note that a positioning of knights on the purple squares leads to every square being covered. Since at least 1 2 knights are needed, and this shows a possible way of covering every square with 1 2 knights, the minimum number of knights needed is 1 2 .