In the game of chess, the Knight can make any of the moves displayed in ... ...
In the game of chess, the Knight can make any of the moves displayed in the diagram to the right. If a Knight is the only piece on the board, what is the greatest number of spaces from which not all 8 moves are possible?
(A) 8
(B) ...
(C) ...
(D) ...
(E) ...
*This question is included in
Nova Press: Set H - Elimination Strategies
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In the game of chess, the Knight can make any of the moves displayed in ... ...
Posted: 12/04/2013 16:12
看不懂啊
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In the game of chess, the Knight can make any of the moves displayed in ... ...
Posted: 02/02/2014 10:48
cannot understand the solution
Contributor
Reply 1 of 1
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Posted: 02/04/2014 11:07
Yao Wen, Jocelyn, this looks like a difficult problem, but it is not.
The Knight (騎士) can move in 8 directions as shown: 2 steps straight and 1 step left or right.
Our job is to find the squares from which the Knight cannot make all 8 moves.
We start with the squares on the edge of the board, since it is obvious the Knight cannot make 2 steps without going the outside of the board. There are 28 of these squares.
Then, we go inside to the next layer of squares. Here, the Knight also cannot make 2 steps without going outside of the board. There are 20 of these squares.
In the next layer of squares, the Knight can make all 8 moves.
Hence, the answer is 20+28=48.
I hope this helps.
