Guarini's Puzzle
There are 4 knights on a chessboard: two white knights at the bottom corners and two black knights at the upper corners.
What is the minimum number of moves required so that the two white knights end up at the upper corners and the two black knights end up at the bottom corners?
The answer is 16.
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1 solution
We should reduce the chessboard into a clearer model: graph.
Let the nodes be cells on the chessboard and an edge exist between nodes if a knight can move between them. We will get a graph like this:
The black and white nodes are where the black and white knights reside. But this graph isn't much helpful than the image itself, let's rearrange the nodes by moving the edges out:
[Omitted central node because it is not connected to any other nodes].
This graph is easier to look and analyse. Notice that we cannot have two knights on each node hence we cannot cross each other. That means every knight have to move in the same direction (clockwise / counter-clockwise) for 4 steps. This answer gives 16.