Friday, 3 January 2014

mathematics - Swapping knights


On a $3\times3$ grid we have:


33grid



with $8$ moves needed to swap the red and blue knights.


What is the minimum numbers of moves to swap the knights on a $4\times4$ grid?


44grid



Answer



It will take:



20 moves to swap the knights



This can be done as follows:




Zerris



All credit goes to @klm123 for demonstrating a good way to visualize this in a similar puzzle.


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