#50
The pawns are more "economical". 1 pawn sacrifice gives 2 (!) half-open lines. Piece sacrifice would give only 1 half-open line. Though you may sacrifice everything, only pawns will allow you to perform 94-moves game. And, as you have to sacrifice 4 pawns in total (-4 half-moves), then the game is limited to 94 moves.
For me it is a simple way to explain a puzzle (together with #39), though I am not sure if you count it as a "proof".
> The pawns are more "economical".
This is not a theorem, this is a heuristic. That is, it is useful when you searching for best result, but completely useless when you proving that the result is really best. Победителей не судят, и неважно, чем они руководствовались, когда принимали решения.
> 1 pawn sacrifice gives 2 (!) half-open lines. Piece sacrifice would give only 1 half-open line.
> though I am not sure if you count it as a "proof".
Of course, it is not proof. There may be 2 pawns on file (double pawn? or how it is in english?), so 1 pawn sacrifice gives 1 half-open lines, not 2.
Ok, I think, that I will leave correct definitions to more experienced people =)
The topic itself is however solved for me, and it was interesting.
I am just interesting: imagine puzzle "mate in 2 moves". Imagine that you have found this mate. And now precisely prove that it was the only way (if so) to mate in 2 moves =)
> I am just interesting: imagine puzzle "mate in 2 moves". Imagine that you have found this mate. And now precisely prove that it was the only way (if so) to mate in 2 moves =)
My personal opinion is that precise proof mostly is not humans occupation: it is computers' occupation.
But, if you try to present a proof, you should try to be as pedantic as computer.
That is, humans may be creative, use heuristics and generate ideas. Computes must understand all this (with human assistance) and generate precise proofs or point to flaws.
BTW, microprocessor design is somewhat similar to this already now. There are automated systems that proof some useful properties of microprocessor designs or generate a counterexamples.
The point is that these precise proofs may be very big and not even intended to be examined by humans.
Just want to share this composition or puzzle
which I forgot to do it and I have remembered today
http://en.lichess.org/WRMZHyZU/white#188 I can not observe your solution because around 17 days ago lichess made a change and now html layout of analysis is broken (for me).