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

Fri Sep 2 05:39:09 EDT 2016

```Can be could stay in us on the notion of speed which would widen this problem to the longer PG.

"Compose the shortest sound checkmate PG witch beat the slowest speed record"

the mat(4,4,0) 9.656854 lenght for 9 plies for example have a speed of :1,0729837...and the lower limit of the speed is ... 1

another kind of stipulation: "what is the the fastest mat" by a knigh alone?"

i have this one : Mat(3,0,7) in 9 plies speed 2,06917/ply
1rbqkbnr/pp1pnppp/3N4/2p5/8/8/PPPPPPPP/R1BQKBNR
solution :
1.Cb1-c3 c7-c5 2.Cc3-d5 Cb8-c6 3.Cd5xe7 Ta8-b8 4.Ce7-f5 Cc6-e7 5.Cf5-d6#

smothered mate

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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