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MatPlus.Net Forum Retro/Math Checkmate By Pam-Krabbe Castling In A Unique PG
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(1) Posted by James Malcom [Tuesday, Dec 3, 2019 03:46]; edited by James Malcom [19-12-03]

Checkmate By Pam-Krabbe Castling In A Unique PG

I've seen Pam-Krabbe castling in plenty of genres, but never in a PG. Simply composing a unique PG that has it is way too easy. Having it end it checkmate is much harder.

Unique PG 11.5
(= 12+13 )

Solution (?): 1. e4 d5 2. exd5 Kd7 3. d6 Kc6 4. Bb5+ Kxb5 5. c4+ Kxc4 6. dxe7 Qxd2+ 7. Bxd2 Kd3 8. Qf3+ Kc2 9. Bh6 Nxh6 10. e8=R Bd6 11. Nc3 Bg3 12. 0-0-0-0-0-0#

This is best effort so far if incorrect, as this is my first dabbling in unique PGs.

The fastest possible checkmate via Pam-Krabbe castling, by my calculations, is 10.5 moves. Feel free to try and create such a unique proof game.
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(2) Posted by Joost de Heer [Tuesday, Dec 3, 2019 11:27]; edited by Joost de Heer [19-12-03]

Simple dual 1. e4 d6 2. e5 Kd7 3. ed6 etc.
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(3) Posted by James Malcom [Tuesday, Dec 3, 2019 15:08]

Oof. Well that should'be been obvious...
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(4) Posted by Andrew Buchanan [Saturday, Dec 21, 2019 07:04]; edited by Andrew Buchanan [19-12-21]

Welcome to the world of proof games, Rewan. Linguistic note: most people called these "PGs" or "SPGs" (shortest) rather than "unique PGs" even though in principle it's more ambiguous. Similarly, people don't call a #2 a "unique mate in 2".

Normally, retros are difficult to validate automatically, but proof games are an exception, and there are several excellent specialist tools available. There are so many dumb and subtle errors possible in proof game design that their support is invaluable. I'm aware of 4 commonly used tools: all are great but have different areas of focus. For fairy problems, you need Popeye or Jacobi, which handle a huge range of fairy conditions, but may be slower for orthodox problems. Popeye is a general purpose engine, not just looking at PGs. Jacobi addresses all help-stipulations and has the ability to add constraints now, which can be a big help. But the problem here although it has a fairy last move basically wants just orthodox checking to validate that (1) there is no orthodox solution (2) if you retract the last move, there *is* exactly 1 solution. For that you want Natch or Euclide. Both are great, but personally I prefer Natch only because Euclide gives up after the first dual is found. Natch presses on, and I find it helpful to know whether there are 2 or 20 or 200 cooks. Like if I'm a golfer, I want to know how far I am from the green so I can pick the right club. Natch doesn't give the mathematically exact number of solutions however, so if you want that in a complicated problem as I have recently (cough New Year cough), you may need to run Natch followed by some shorter runs in Jacobi or Popeye.

As always though with good tools, one needs to avoids dependency. These tools give validation not creativity. Also, a problem composed by hand has maybe more logic to it, and is perhaps more fun to solve.

There are other experts here who will no doubt have much wiser things to say about proof game engines than I. In the mean time, Natch validated this for me:

(= 12+14 )
SPG in 12.5
(James Malcom + Andrew Buchanan)

There is also a 10.5 with extraneous promoted rook (rnb2bnr/ppp2ppp/8/3p4/3P4/2N1KQ2/PPk1RPPP/R5NR), validating your time estimate.
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(5) Posted by James Malcom [Saturday, Dec 21, 2019 15:38]; edited by James Malcom [19-12-21]

Nice job Andrew!

The solution isn’t too hard to find actually. I won’t post the solution though.
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(6) Posted by Joost de Heer [Tuesday, Dec 24, 2019 14:50]

Even better would be an SPG which is cooked in X moves with a regular rook on the 8th rank, and a unique solution with a promoted rook, and mate with X+1. OOOOO#
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(7) Posted by Andrew Buchanan [Monday, Jan 4, 2021 20:01]

There is also a 10.5 with extraneous promoted rook (rnb2bnr/ppp2ppp/8/3p4/3P4/2N1KQ2/PPk1RPPP/R5NR), validating your time estimate

This is cooked: there are two ways forward from the 8.0 point. d2-d4 can transpose with the P-K. However the other thread offers a fixed version. Have to be careful about this, as running Natch to the point just before the supposed P-K mate move won't pick this up
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MatPlus.Net Forum Retro/Math Checkmate By Pam-Krabbe Castling In A Unique PG