[Retros] PGs with two or more solutions: Solution differences

afretro afretro at yandex.ru
Thu Feb 5 07:11:30 EST 2004

Hi folks,
I▓d like to touch upon three points today.
First: In connection with the current exchange of opinions on how different two (or more) solutions of an (S)PG must be in order for the position/diagram to qualify as a ⌠genuine■ two-/multi-solution (S)PG, I▓d like to inform you that about a decade ago I published an article called Novelty: A Formula to Estimate Two-solution Proof Games (diagrammes, Numero Special 15, Juillet-Septembre 1994). In that article I proposed a formula for evaluating two-solution PGs. The formula is quite arbitrary, of course; the relationships among the parameters involved, as well as the list of parameters, can be different. I just wanted to point to the fact that a purely mathematical approach could be used to evaluate the extent of dissimilarity between the solutions of a two-line PG. Here is what the formula looked like:
Nl Nz
E = (_____ + ____) x Nt,
Nz+Nt Nt

E being the estimate, Nt being the total number of single moves in the two solutions (taking into account the fact that the two solutions may be of different length; i.e., Nt = N(1st solution) + N(2nd solution)), Nl being the number of ⌠absolutely non-coinciding,■ ⌠unique■ single moves in the two solutions (regardless of move number) (meaning that Qd1-e1 is not the same as Qc1-e1 or Qd1xe1), and Nz being the number of ⌠partially coinciding■ moves) (moves differing in ordinal number only, e.g. 12.Qd1-e1 vs. 13.Qd1-e1).
Any ideas for a better, more convenient, less clumsy formula?
Second: What Francois has been engaged in clearly shows that the work of any PG-maker amounts, in a certain sense, not to composing proof games but to extracting, one by one, some interesting ⌠helpgames■ from a huge yet finite pool of ⌠potentially existing■ PGs. Accordingly, from ⌠the philosophical viewpoint,■ we can be looked upon, not as PG authors/creators but rather as PG discoverers.
And finally, here is a third, unrelated point: R345 by Cedric Lytton (The Problemist, January 2004) appears to be cooked. Would a report on the cook to the Retro Corner be the right thing to do, or should I send a personal message to Dr. Lytton?
Yours most sincerely,
Andrey Frolkin
Kiev, February 5, 2004