Puzzle 7: Chess moves

I thought I’d add a puzzle I was not able to solve myself, but turned out be rather straightforward in the end.

In chess, the most interesting piece is often the knight or horse. This is the only unit able to leap above other units and go beyond moving in straight lines. The knight can move one step forward/back and 2 steps left/right or alternately 2 steps forward/back and 1 step left/right. The figure below shows the tiles a knight can move to in the next turn.

knightChessMove

The question is how many knights can you fit on a chess-board so that no knight can move so as to land on another knight’s square in its next move?

Note: Chess is played on an 8*8 board. Therefore there are 64 squares in total with 32 black and 32 white ones.

.

.

.

.

.

The key thing to realise is that as in figure above, if the knight is sitting on a black square, then whichever direction it moves in, it will land on a white square. So if we fill all 32 black squares with knights (or all 32 white squares) then no knight can land on any other. Now if we add any extra knights on a white (black) square then in its next move it will have to land on a black square which is already occupied by another knight.

Hence we can fit 32 knights so that no knight can threaten another in the next move.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s