Solution error for the proof by induction
	   of the "Eye color" conjecture

   The general recommendation: If you see that your proof
contradicts to facts, then you "execute" CAREFULLY this
proof for THE CASE where it contradicts.

   For our problem, the sensitive case is two persons.
Indeed, if for any pair, the eye color is the same, we agree
that it is the same for all. However, WHY it is the same for
any pair??

   Let us follow the proof given in the class, for n+1=2.
We know that for any single person (n=k=1), there is a unique
eye color. Now, we take TWO persons (n=k+1=2), order them
in a line, and say:

 - there is a unique eye color for the FIRST k-1(=1) persons,
   by the induction assumption;
 - there is a unique eye color for the LAST k-1(=1) persons,
   by the induction assumption;
 - observe that both colors are the same(?), since it is
   the eye color of anyone out of the middle k-2(=0) persons,
   i.e. those except for the first and the last one.

Here is the error: if k-2=0 then there is NO such person.

18.12.02
		Yefim Dinitz