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Q: Riddle ( Answered 5 out of 5 stars,   2 Comments )
Subject: Riddle
Category: Miscellaneous
Asked by: aj9989-ga
List Price: $2.00
Posted: 09 May 2006 23:07 PDT
Expires: 08 Jun 2006 23:07 PDT
Question ID: 727192
A drawer contains a number of red and blue socks.  If I pull two out
at random, then their chance of being a red pair is one half and their
chance of being a blue pair is one twelfth.  How many socks are in the
drawer?  How many of each color?
Subject: Re: Riddle
Answered By: denco-ga on 10 May 2006 00:01 PDT
Rated:5 out of 5 stars
Howdy aj9989-ga,

Bryan (probonopublico-ga) speaks a certain truth in his comment, as there
are an odd number of red and blue socks in the drawer.

One of "Ken's Puzzle of the Week" has the solution to your riddle.

"85 red, 35 blue"

The above page also provides the formula that we need to prove this.

We have to find a and b integers representing respectively the numbers
of red and blue socks such as:

a*(a-1)/(a+b)*(a+b-1) = p   (1)
b*(b-1)/(a+b)*(a+b-1) = q   (2)

If we take the first formula for the red socks, we get:

85*84/120*119 = 7140/14280 = 1/2

We can then apply the second formula to prove the blue socks solution:

35*34/120*119 = 1190/14280 = 1/12

If you need any clarification, please feel free to ask.

Search strategy:

Google search on: red blue socks drawer

Looking Forward, denco-ga - Google Answers Researcher
aj9989-ga rated this answer:5 out of 5 stars and gave an additional tip of: $1.00

Subject: Re: Riddle
From: probonopublico-ga on 09 May 2006 23:25 PDT
This is impossible to answer because there is always at least one sock missing.
Subject: Re: Riddle
From: denco-ga on 10 May 2006 11:47 PDT
Thanks for the 5 star rating and tip, aj9989-ga.

Looking Forward, denco-ga - Google Answers Researcher

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