GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Dec 2019, 00:54

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59720
In the game of chess, the Knight can make any of the moves displayed  [#permalink]

### Show Tags

21 Jun 2017, 02:10
1
9
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:58) correct 34% (01:45) wrong based on 114 sessions

### HideShow timer Statistics

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 [ 14.4 KiB | Viewed 3980 times ]

_________________
Current Student
Joined: 18 Aug 2016
Posts: 593
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: In the game of chess, the Knight can make any of the moves displayed  [#permalink]

### Show Tags

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
_________________
We must try to achieve the best within us

Thanks
Luckisnoexcuse
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3305
Location: India
GPA: 3.12
In the game of chess, the Knight can make any of the moves displayed  [#permalink]

### Show Tags

21 Jun 2017, 02:23
1
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)
_________________
You've got what it takes, but it will take everything you've got
Director
Joined: 13 Mar 2017
Posts: 730
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
In the game of chess, the Knight can make any of the moves displayed  [#permalink]

### Show Tags

22 Jun 2017, 01:03
2
Bunuel wrote:

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

Retired Moderator
Joined: 22 Aug 2013
Posts: 1409
Location: India
Re: In the game of chess, the Knight can make any of the moves displayed  [#permalink]

### Show Tags

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
Intern
Joined: 05 Nov 2019
Posts: 1
Re: In the game of chess, the Knight can make any of the moves displayed  [#permalink]

### Show Tags

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.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8692
Location: United States (CA)
Re: In the game of chess, the Knight can make any of the moves displayed  [#permalink]

### Show Tags

19 Nov 2019, 19:18
1
Bunuel wrote:

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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: In the game of chess, the Knight can make any of the moves displayed   [#permalink] 19 Nov 2019, 19:18
Display posts from previous: Sort by