[Retros] Distance-PG = Fastest "n"

[Francois Labelle]

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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