Discussion
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? 
*This question is included in Nova Press: Set H - Elimination Strategies, question #6
| (A) | 8 |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 12/04/2013 16:12
看不懂啊
Posted: 02/02/2014 10:48
cannot understand the solution
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.
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.