Interesting one... Two squares are chosen at random on

Question

Interesting one... :-D 

Two squares are chosen at random on a chessboard. What is the probability that they have a side in common?

(A) 1 / 18 
(B) 64 / 4032 
(C) 63 / 64 
(D) 1 / 9 
(E) 21 / 57

BG · Answer

WE HAVE 112( 56 in rows and 56 in columns) pairs of squares with side in common. 64C2=2016. then required prob is 112/2016=1/18 or A)

Yurik79 · Answer

good one! vivek))hope that I won't come across such quest. on real exam. But what if I don't know how many squares where are on the chessboard? BTW couldn't solve it Nice explanation BG :cool

you RULE

peterlude · Answer

Yep. This questionis unrealastic. I'm not a chest player, hence i wouldn't know how many squares the board has. Unless you're given this information, you could easily dispute this question to GMAC.

chuckle · Answer

I got an answer of 7/128 (which is not in answer choices

) My logic is: THere are three types of squares: 1. 4 Corners - These have exactly two other squares with a side common. 2. Along borders exluding corners - These have exactly three squares with a side common - 24 squares 3. All the other squares - These have exactly four squares with a side common - 36 squares. Now, I tried to write the equation for all these cases. After simplifying, I get 7/128. I know that answer is wrong. Can you guys explain why?

vivek123 · Answer

Here we go,

1) There total 64 squares on a chess board, arranged in 8*8 form
2) There are 4 corner squares where only 2 other squares share a side so total number of ways for such a square = (4*2)
3) There are 24 squares touching the boarder of the chess board (excluding 4 corner squares) where 3 other squares share a side.
=> (24*3)
4) There are remaining 36 squares where 4 other squares share a side => (36*4)

So, total number of ways in which a square can be selected with one side shared is = (4*2) + (24*3) + (36 * 4) = 224

& total number of ways in which a square can be selected = 64*63 

So, probability of selecting one square such that one of it sides is in common =  224/(64*63) = 1/18

chuckle · Answer

Thanks for the explanation Vivek. Atleast my approach is right.

vivek123 · Answer

Yeah :-D Your approach is correct! :good

Interesting one... Two squares are chosen at random on

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