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In the game of chess, the Knight can make any of the moves displayed

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In the game of chess, the Knight can make any of the moves displayed  [#permalink]

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New post 21 Jun 2017, 02:10
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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) 24
(C) 38
(D) 48
(E) 56

Attachment:
2017-06-21_1308.png
2017-06-21_1308.png [ 14.4 KiB | Viewed 3980 times ]

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Re: In the game of chess, the Knight can make any of the moves displayed  [#permalink]

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New post 21 Jun 2017, 02:22
IMHO Counting is much easier method

We know that the Knight requires three spaces on all its sides to move.hence counting the two vertical columns on both the side (leftmost and rightmost) gives us 16*2 = 32

Counting the leftover top and bottom spaces (8 * 2 = 16)

Adding gives us 48 hence D

Please correct me if i am wrong
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In the game of chess, the Knight can make any of the moves displayed  [#permalink]

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New post 21 Jun 2017, 02:23
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The only positions from where the Knight can move in all directions,
as shown in the figure are the 4*4 matrix(of squares)

In the extreme rows and columns, moves in a maximum of 4 directions are possible.
In the rows and columns inside the extreme row, moves in a maximum of 6 directions are possible.
Hence, the number of squares from which all of these moves are possible are 4*4 = 16
Since the chess board has 64 squares,
64-16(48) squares is the greatest number where all of these moves are not possible(Option D)
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In the game of chess, the Knight can make any of the moves displayed  [#permalink]

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New post 22 Jun 2017, 01:03
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Bunuel wrote:
Image
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) 24
(C) 38
(D) 48
(E) 56

Attachment:
2017-06-21_1308.png


We can solve it by just counting the boxes..
Anyway the logic behind counting and calculation is given below..

From the picture it is very clear that the Knight can take all the 8 moves only if it is not in the last 2 rows or columns of the board.
So lets calculate the number of spaces where all the 8 moves are not possible.

Last row an column : (8+8+6+6)= 28
Penultimate row and column : (6+6+4+4) = 20

Total = 28+20 =48

Answer D.
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Re: In the game of chess, the Knight can make any of the moves displayed  [#permalink]

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New post 22 Jun 2017, 01:42
Chess board has '64' squares.

To have ALL 8 moves possible, from the reference point of knight's square, there should be movement of 2 steps feasible in each direction - meaning 2 places above, 2 places below, 2 places right and 2 places left. If these conditions are met, then all 8 moves will be possible.

If we look at the outermost 8 by 8 matrix (leftmost column, rightmost column, top row and bottom row) - we can easily decipher that many of those 8 moves wont be possible from any of those squares.

Now lets look at the 6 by 6 matrix (second column from left, second column from right, second row from top and second row from bottom), here also we can decipher that all 8 moves wont be possible from any of these squares.

Now lets similarly move to 4 by 4 matrix. Here all 8 moves will be possible - because there are 2 places to left, right, above and below available. Inside these also, from all these squares, 8 moves will easily be possible.
So all 8 moves are possible from these interior '16' squares.

Our required answer = 64 - 16 = 48. Hence D
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Re: In the game of chess, the Knight can make any of the moves displayed  [#permalink]

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New post 05 Nov 2019, 11:23
Interesting problem, especially because I love to play chess. There are programs called "chess engines", that can help to find best move, for example Stockfish.
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Re: In the game of chess, the Knight can make any of the moves displayed  [#permalink]

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New post 19 Nov 2019, 19:18
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Bunuel wrote:
Image
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) 24
(C) 38
(D) 48
(E) 56

Attachment:
2017-06-21_1308.png



If the Knight is located at a space (i.e., square) that is either on the border of the chessboard or next to a square that is on the border of the chessboard, then not all 8 moves by the Knight are possible. The number of spaces that are on the border of the chessboard is 8 x 4 - 4 = 28, and the number of squares that are next to a square that is on the border of the chessboard is 6 x 4 - 4 = 20. Therefore, there are 28 + 20 = 48 such spaces from which not all 8 moves are possible.

Answer: D
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Re: In the game of chess, the Knight can make any of the moves displayed   [#permalink] 19 Nov 2019, 19:18
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