# [Retros] Retros Digest, Vol 146, Issue 3

Fri Sep 2 07:46:52 EDT 2016

```searching for the challenge of « Knights alones»

"Compose a sound checkmate PG wicth "maximize" the geometric score = c*sqr(5) - (α + β*sqr(2)) "

I find a Mat (1,0,12) ! A single movement is not made by a Knight! it's the minimum ( very proud of that :P )

"Mat (1,0,12) : what is the final move?"

solution:
r1bqkn1r/pp1pnpNp/2p5/8/8/8/PPPPPPPP/R1BQKBNR
1.Cb1-c3 Cb8-c6 2.Cc3-d5 Cc6-e5 3.Cd5xe7 c7-c6 4.Ce7-g6 Cg8-e7 5.Cg6xf8 Ce5-g6 6.Cf8-e6 Cg6-f8 7.Ce6xg7#
13 plies

the length is 27,8328157 and the speed 2,1409858/ply
but the score ( « Knights alones» ) is 1,987139 (for the limit-max is sqr(5)=2.23606 ) = 88,86% of the max

Dominique.

> Message du 02/09/16 07:42
> De : retros-request at janko.at
> A : retros at janko.at
> Copie à :
> Objet : Retros Digest, Vol 146, Issue 3
>
> I wrote:
>
> < What about *minimum* geometric length? Here it may
> < be possible to prove that one has the absolute minimum (if it's small
> < enough that anything beyond the search bounds must be longer).
>
> Francois Labelle  replied:
>
> > You're right, it's possible.
>
> > The minimum geometric length for a sound checkmate PG is
> > 9.656854 = (4,4,0), so the proof of optimality only required searching
> > up to ply 9.
>
> > Only one sound checkmate PG achieves it: [...]
>
> Great!
>
> andrew buchanan  writes:
>
> > > The second-shortest is 10.242641 = (6,3,0)
>
> > > So I guess someone could ask:
> > > "Compose a sound checkmate PG with geometric length less than 10".
>
> > This unnecessarily removes the case 10.
>
> > I would prefer the more whimsical stipulation:"Compose a sound
> > checkmate PG with geometric length less than 10.24264."
>
> Normally "geometric length at most 10", though "length less than
> 6 + sqrt(18)" hints at the runner-up length too.
>
> NDE
>
>
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