A Bowdlerized Conundrum

From: r.e.s. (r.s_at_ZZmindspring.com)
Date: 02/18/05 

Date: Fri, 18 Feb 2005 23:47:03 GMT

In a group of people there are m men and w women.
Each person must shake hands with every person of
the opposite sex. However, everyone is paranoid
about germs, so one or more gloves must be used in
each handshake, so that no one is contaminated by
anyone else (not even indirectly by touching a
surface someone else has touched, nor by touching
a surface that has touched a surface that someone
else has touched, etc.). Let the minimum number
of gloves required be g(m,w).

Example: Only 2 gloves are needed for 3 against 1
( g(1,3) = g(3,1) = 2 ) ...
For m=3 and w=1, with * marking each handshake:

         W1* W1* W1*
Glove1 ------ ------ ------
                       M2* M2
                                     M1
Glove2 ------ ------ ------
         M1* M1 M3*

The sequence g(m,1)(m >= 0) begins 0,1,2,2,3,...
(1) How does the remainder of the sequence go?
(2) How about g(m,2)(m >= 0)?
(3) Is there a formula for g(m,w)(m >= 0, w >= 0)?

--r.e.s.

Relevant Pages

  • Re: Nate on Early Show Monday
    ... It was the famous "GE Handshake." ... had just bought NBC and Dave went to the GE headquarters with a camera ... tried to shake hands with the security goon and the security goon ... refused to shake hands and moved his hand away and kicked them out. ...
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  • Re: NYC: Hasidic actor walks off Portman movie
    ... saying it's _only_ between men and women is patently false. ... But if they ever see a religious man shake hands with a man, ... having to go into lengthy explanations. ... There are two situations which call for a handshake. ...
    (soc.culture.jewish.moderated)
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