Homework Help: Math

Posted by May on Wednesday, November 4, 2009 at 8:00pm.

In chess, a knight can move either two squares horizontally plus one vertically or two squares vertically plus one horizontall.
a) If a knight starts from one corner of a standard 8*8 chessboard, how many different squares could it reach after
i) one move?
ii) two moves?
iii) three moves?

Math - PsyDAG, Thursday, November 5, 2009 at 9:59am
From the corner, it could only reach 2 squares in the first move. In the center of the board, it can reach 8 different squares. However, in the second move, you have two different starting points, but they don't have the availability of all eight positions due to the edge of the board. Also, since the problem is phrased as "different squares," you cannot include the square(s) it was previously in.

I would suggest using a chessboard to deal with this problem.

I hope this helps. Thanks for asking.

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