Combinations (1 Viewer)

[goobi]

A chessboard has 64 squares arranged in eight rows of eight. The only moves that a King may make are from the square on which he is standing to an adjacent square. Find the total number of moves from all possible positions that the King can make on a chessboard.

The answer is 420 moves but I have no idea how to solve it.

Thanks for any help in advance!

 

[lolcakes52]

Okay so a king can move into any of the squares that it is surrounded by aka the surrounding 8 squares. Now we split the board into 4 parts, a six by six grid in the middle, the four corners and the remaining parts of the edges, which are each a row six squares long.

For the six by six grid the king can move into any of the surrounding squares so the total number of moves in this area is 6*6*8=288
For the four corners the king can only move into 3 of the surrounding squares so the total number of movies in this area is 4*3=12
For the remaining edge's the king can only move into 5 of the surrounding squares and there are four of these areas so the total number of moves is 4*6*5=120

Now we add these together and bam 420.

 

[goobi]

Thanks!