[Retros] About T.Orban problem; Yefim's letter 01/12/2005

[Seth Breidbart]

Nicolas.Dupont at math.univ-lille1.fr wrote:

>>> Question : is it possible to go one step further ? that is several

>>> solutions in N and N+1 moves, but only one solution in N+2 moves ?

>>

>> No.  Start by popping a knight out and back; that turns any solution

>> in N moves into 16 solutions in N+2 moves.

>>

> Of course, I thought about that possibility. And it doesn't prove that the

> answer to my question is obviously No. For example,  let's consider a pg

> where it is impossible to start by popping a knight.


After 2 moves, you're back to the opening position, the only
difference being that it's 2 moves later.  That matters only if the 50
move rule applies, which means no captures or pawn moves.

If N+2 is over 50, the 50 move rule stops it, whether you start by
popping knights or not.

If N+2 is under 50, the 50 move rule doesn't apply.

So I still don't see how it can matter.

Seth