Math Is Fun Forum

juantheron

Member

Registered: 2011-10-19

Posts: 312

chess problem

2 small square are choosen at random at random from a chess board then the probability that they have exactly one common vertex

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: chess problem

hi juantheron

i got 1/18.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: chess problem

but answer given is

options

(1) 7/288              (2) 23/504        (3) 23/252      (4) 7/144

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: chess problem

oh,sorry i think i misread the problem.i thought it said edge

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: chess problem

hi juantheron

i think the answer is 4) but the probability that i am right is the solution to this problem.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: chess problem

There are three types of squares on a chess board: a) those with an adjacent square on all 4 vertices, b) those with an adjacent square on 2 vertices, and c) those with an adjacent square on just 1 vertex.  There are 36 squares of type a), 24 of type b), and 4 of type c).  If a type a) square is chosen first there is a 4/63 chance that the second square will be corner adjacent to it, if a type b) square is first then there is a 2/63 chance that the second square will be corner adjacent, and a type c) square has a 1/63 chance.  This gives us a total probability of (36/64 * 4/63) + (24/64 * 2/63) + (4/64 * 1/63) = 49/1008 = 7/144.

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Wrap it in bacon

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: chess problem

thanks anonimnystefy  and   dude

(triying to understand that)