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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 2335 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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Re: In the game of chess, the Knight can make any of the moves displayed &nbs [#permalink] 31 Jul 2018, 05:51
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