🚀 go-pugleaf

Here is a simple game played with two counters.  You name a number
(non-negative integer), and then your opponent names a different number.
These are the initial values of the two counters.

The general move is to decrease one of the counters by either 2, 4, or 7.
However, you can't make a counter negative.  Once a counter gets to 0 or 1, it
can't be changed any more.  The game is over when both counters are like this,
and the last person to move is the winner.

I claim there is a unique winning move.  What is it?  Show that after your
opponent names his number, the correct move is always to decrease the number
you named.  Also, explain what that move is based on what your opponent named.

If you've read _Winning Ways_ and you're going to use Nim-values to figure
this out, this puzzle is too easy for you.  I want the game to be explained so
that a small child could win.

--
Joe Keane, amateur mathematician
jgk@osc.com (uunet!amdcad!osc!jgk)