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

Question

https://gmatclub.com/forum/download/file.php?id=35876 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 2017-06-21_1308.png

Luckisnoexcuse · Answer

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

pushpitkc · Answer

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)

shashankism · Answer

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.

amanvermagmat · Answer

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

andrewmax · Answer

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.

ScottTargetTestPrep · Answer

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

BrushMyQuant · Answer

Now, for a Knight to be able to move 8 possible moves the Knight should have at least 2 squares in each direction to be able to complete that.
This means that the knight cannot be in any of the squares where we don't have at least 2 squares to move in each direction possible.
So, the Knight cannot be in rows 1,2,7,8 and columns a,b,gh

Refer Below Image

Attachment:

squares.jpg [ 35.21 KiB | Viewed 2809 times ]

This means that the Knight can be there only in the center blue squares, which are 4*4 = 16

So, the greatest number of spaces from which not all 8 moves are possible = 64 - 16 = 48

So, Answer will be D
Hope it helps!

If you want to play a "friendly" game of chess then invite me for game on chess.com, my profile link here!

Rance14 · Answer

https://gmatclub.com/forum/download/file.php?id=82557 Taking the above diagram as a sample chessboard The knight moves in "L"s As you can see if you place the knight in any of the blue dotted squares - the knight will be able to make all 8 moves But if you put the knight in any of the red or green dotted squares - the knight will not be able to make all 8 moves Hence counting the green and red dottes squares = 28 + 20 = 48 Squares (answer) GMAT-Club-Forum-h49b6k85.png

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

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