Re: Coin puzzle (spoiler)

[mjd-perl-pm@plover.com]

> What's your strategy for flipping the coins?



























I think I know how to do it in ad most seven moves.  

Summary:  NS, NE, NS, N, NS, NE, NS  will win from any configuration.

1. My goal is to make a '+' configuration, where north and south are
   in one state and east and west are in the other state:

        H        T
       T T  or  H H     '+'
        H        T

If I can make a +, then I can call 'NS' and win.

2. Suppose  I have an '=' configuration, there there are two heads and
   two tails, but north and south show different sides:

        H        H
       H T  or  T H    '='
        T        T

Then I can call 'NE'.  This either wins immediately or gets me a '+',
from which I can win in one move.

3. Suppose I know I have two heads and two tails.  Then there must be
   either an '=' or a '+'.  If I call 'NS', then I win if there was a
   +, and if I didn't, there must have been an =.  If there was an =
   before, there is still an = after the 'NS'.  So now I know I have
   an '='  and I can win in at most two moves.

4. Initially, I either have two pairs, three of a kind, or four of a
   kind.  If there's four of a kind I win instantly.  So I must have
   three of a kind or two pairs.  I know (from 3. above) that if I
   call 'NS', 'NE', 'NS', I will win if I began with two pairs.  If I
   haven't won after doing that, I know that I had three of a kind to
   begin with, and, because I always flipped the coins in pairs, I
   still have three of a kind.

   Then I can call 'N', and either I flip the odd coin and win
   immediately or else I now have two pairs and I can win in three
   moves as per 3. above.

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