BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Knight Moves - Chess

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 966
Joined: Sat Jan 02, 2010 8:06 am
Thanked: 230 times
Followed by:21 members

Knight Moves - Chess

by shankar.ashwin » Sun Nov 13, 2011 3:54 am
In the game of chess, the Knight can make any of the moves displayed in the diagram. 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
Attachments
Knight.jpg
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 588
Joined: Sun Oct 16, 2011 9:42 am
Location: New Delhi, India
Thanked: 130 times
Followed by:9 members
GMAT Score:720

by rijul007 » Sun Nov 13, 2011 4:09 am
For Knight to be able to make all 8 moves.. it should be atleast 2 blocks away from each edge..
So the number of blocks where it can make all 8 moves are = (8-4)^2 = 16

Number of blocks from where all 8 moves are not possible are = 8^2 - 16 = 64-16 = 48

Option D
Top
User avatar
Community Manager
Posts: 1060
Joined: Fri May 13, 2011 6:46 am
Location: Utrecht, The Netherlands
Thanked: 318 times
Followed by:52 members

by neelgandham » Sun Nov 13, 2011 4:12 am
Knight can make all the moves displayed in the diagram only if it is in the squares left in white(In the diagram) = 4*4 = 16

Total number of squares = 8*8 = 64

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

IMO D
Attachments
knight_194.jpg
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Top
Newbie | Next Rank: 10 Posts
Posts: 6
Joined: Sun Jul 08, 2012 1:09 am

by mneeti » Thu Sep 04, 2014 10:24 am
Can someone please help me understand this question and the solution?
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Sep 04, 2014 11:36 am
shankar.ashwin wrote:In the game of chess, the Knight can make any of the moves displayed in the diagram. 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
Since a chessboard is 8 by 8, the total number of positions on a chessboard = 8*8 = 64.
GOOD positions for the knight = 64 - BAD POSITIONS FOR THE KNIGHT.
Here, a BAD position is one from which the knight can be make all of the moves shown in the diagram.

In the diagram, the knight is positioned at the CENTER OF A 5 BY 5 SQUARE..
Implication:
To be able to make all of the moves shown in the diagram, the knight must be at the CENTER OF A 5 BY 5 SQUARE, as shown here:
XXXXXXXX
XXXXXXXX
XXKXXXXX
XXXXXXXX
XXXXXXXX
XXXXXXXX
XXXXXXXX
XXXXXXXX

Count how many 5 by 5 squares can be formed from the 64 positions on a chessboard.

If row 5 provides the bottom of the 5 by 5 square, we get the following options.
XXXXXXXX
XXXXXXXX
XXKXXXXX
XXXXXXXX
XXXXXXXX
XXXXXXXX
XXXXXXXX
XXXXXXXX

XXXXXXXX
XXXXXXXX
XXXKXXXX
XXXXXXXX
XXXXXXXX
XXXXXXXX
XXXXXXXX
XXXXXXXX

XXXXXXXX
XXXXXXXX
XXXXKXXX
XXXXXXXX
XXXXXXXX
XXXXXXXX
XXXXXXXX
XXXXXXXX

XXXXXXXX
XXXXXXXX
XXXXXKXX
XXXXXXXX
XXXXXXXX
XXXXXXXX
XXXXXXXX
XXXXXXXX
Total number of options = 4.

If row 6 provides the bottom of the 5 by 5 square, there will be 4 more options.
If row 7 provides the bottom of the 5 by 5 square, there will be 4 more options.
If row 8 provides the bottom of the 5 by 5 square, there will be 4 more options.

Thus:
The total number of 5 by 5 squares that can be formed = 4+4+4+4 = 16, implying that there are 16 BAD positions from which the knight can make all of the moves shown in the diagram.
Since there are 16 bad positions, the total number of GOOD positions = 64-16 = 48.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

by GMATinsight » Fri Sep 05, 2014 10:15 am
shankar.ashwin wrote:In the game of chess, the Knight can make any of the moves displayed in the diagram. 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
I guess it's pretty simple this way.

For a knight to have all 8 moves possible the square where it is located should be atleast 2 rows away from topmost row, 2 rows away from bottom-most row, 2 columns away from rightmost column and 2 columns away from left-most column.

Therefore all 16 blocks (as shown in figure within red boundaries) are possible blocks from where all 8 moves for a knight are possible.

Therefore remaining blocks from where all 8 moves are not possible = 64-18 = 48

Answer: Option D
Attachments
Solution 67.jpg
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Mon Nov 11, 2019 1:26 pm
shankar.ashwin wrote:In the game of chess, the Knight can make any of the moves displayed in the diagram. 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
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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1