[Retros] Distance-PG = Fastest "n"

[Eric Angelini]

Many thanks, François, this is what I was looking for !

> length of a + b*sqrt(2) + c*sqrt(5)

... this is what I like too: those a, b and c give just
the right amount of information about the game (strait
one-square movements, oblique one-square movements, jumps).

> tempting to use sqrt(2)-1 to retroactively shrink the previous move.

... brilliant idea !

Merci encore !
É.




De : Retros [mailto:retros-bounces at janko.at] De la part de Francois Labelle
Envoyé : dimanche 28 août 2016 21:37
À : retros at janko.at
Objet : Re: [Retros] Distance-PG = Fastest "n"

Hi Eric,

If I programmed things correctly, then these problems should have unique solutions:

ply 5
  6,5,0

ply 6
  2,6,0
  3,6,0 (similar to previous)
  3,8,0
  3,9,0 (similar to previous)
  3,10,0 (similar to previous)
  3,11,0
  6,11,0
  8,2,0
  9,6,0 (similar to 3,6,0)
  10,7,0 (similar to 6,11,0)

where a,b,c means "find a game with total move length of a + b*sqrt(2) + c*sqrt(5) ending in checkmate".

I also found problems with unique solutions without the "checkmate" condition:

ply4
  5,0,2
  7,4,0

ply5
  5,5,2

ply6
  14,9,0
  16,6,0
  16,7,0
  16,8,0
  17,5,0

For example, the solution to "ply4 5,0,2" is "1. Nc3 d5 2. Nxd5 Qxd5".

There's still the question of the length of an e.p. capture. I assumed sqrt(2), blindly using the maximummer definition (see "length of a move" from http://christian.poisson.free.fr/problemesis/condus.html which doesn't say anything special about e.p.). But in this case, because we're adding all the lengths, I admit that it's tempting to use sqrt(2)-1 to retroactively shrink the previous move.

    François
On 28/08/16 12:15 PM, Eric Angelini wrote:

The herunder game ending in checkmate
has the same length 4(1+SQR2) as
the "Black version" seen before:
1. e2 -- g5
2. Be2 -- f6
3. Bh5++
But this checkmate is not as fast as
the Black's one. So what do "fast"
and "fastest" mean? Well, this deals
obviously with the quantity of moves.
If this type of problem has no name,
it could be baptised "Fastest n" --
"n" being a quantity in square-side
units.
At least this type of problem doesn't
need any diagram -- what a relief for
printed magazines !-))


Le 28 août 2016 à 17:08, Eric Angelini <Eric.Angelini at kntv.be<mailto:Eric.Angelini at kntv.be>> a écrit :
For instance, the fastest Distance-PG
of total length 4(1+SQR2) ending in checkmate comes of course after the
well known:
1.f3 -- e6
2.g4 -- Qh4++
... but as the White moves can be
exchanged, this is not a unique
solution.
à+
É.
Catapulté de mon aPhone


Le 28 août 2016 à 16:20, Eric Angelini <Eric.Angelini at kntv.be<mailto:Eric.Angelini at kntv.be>> a écrit :
Yes Roberto,
a sound proof game of this (total) length,
and, in my dreams, the shortest one,
hopefully unique, I have in mind.

More generally, one can assign for
any past, present and future a single
such number, if I'm not wrong.
It would be nice to have unique
numbers "n" for precise tasks like:
-find the SPG of total length "n" ending in a checkmate;
-find the SPG of total length "n"
with a casling;
-find the SPG of total length "n"
with an en passant capture, etc.
BTW, what would be the geometrical
length of an e.p. capture?
But this is old hat, I'm sure, no?
à+
É.
Catapulté de mon aPhone


Le 28 août 2016 à 13:53, roberto osorio <osorio.arg at gmail.com<mailto:osorio.arg at gmail.com>> a écrit :
Hi Eric,

with SQR5 you surely mean a knight move, so the PG has to include 6 knight moves plus  straight displacements total 20 long.

Many unsound sequences  fit whit these requirements. When you say "Find a PG", do you mean "a sound PG"?

best,
Roberto Osorio




2016-08-27 10:17 GMT-03:00 Eric Angelini <Eric.Angelini at kntv.be<mailto:Eric.Angelini at kntv.be>>:

Hello Retro-fans,
This is for sure old hat, but do you know
a nicer example than my attempt
to produce an unique solution?

"Find a PG ending in checkmate where the pieces have  browsed
the distance of 20 + 6SQR5 units"

(read "twenty plus six times the
square roots of five" - the unit being
the side of a square, of course)
Best,
É.


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