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Horse exchange

Horse exchange

The image shows two black horses and two white horses. The objective of the game is to exchange the horses with each other so that the white horses are on the right occupying the positions that initially occupy the black horses and vice versa.

How many movements do you need?

Solution

The following image shows numbered boxes on which horses can move. In the circular diagram on the right are the possible movements to move from one square to another, so we will need a minimum of 16 movements to be able to exchange the four horses with each other.

If we move clockwise, the movements would be:
1→5, 6→2, 8→4, 3→2, 5→6, 2→8, 4→3, 7→1, 1→5, 6→2, 8→4, 3→2, 5→6, 2→8, 4→3, 7→1