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

roberto osorio osorio.arg at gmail.com
Fri Sep 2 08:29:59 EDT 2016

```Hi Dominique,

Three geometrical types of moves: orthogonal, (2,1), diagonal, i.e., N,
SQR5, SQR2.
Due to the opening, the task of 100% moves of just one type for a checkmate
is only feasible for (N,0,0).

I found a sound one in 14 single moves. Is there some one shorter? Surely
this is easy to asnwer for Francois.

2016-09-02 8:46 GMT-03:00 Dominique Forlot <dominique.forlot at wanadoo.fr>:

>
> 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.
>
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>
>
> > 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 <flab at wismuth.com> 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 <andrew at anselan.com> 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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