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1 problem(s) found in 2248 milliseconds (displaying 1 problem(s)). [PROBID='P1338411'] [download as LaTeX]

1 - P1338411
Andrew Buchanan
Retros mailing list 2/1/2017
P1338411
(16+16) C+
PG in 10.0
How many solutions?
e.g. 1. Sc3 b5 2. Se4 Lb7 3. Sg5 a5 4. e4 Ta6 5. Le2 Te6 6. Lg4 Te5 7. S1f3 e6 8. 0-0 De7 9. h4 Dd6 10. h5 Da6
play all play one stop play next play all
2017 Lösungen
Henrik Juel: The 10 white moves come in two sequences:
Sc3-e4-g5.e4.Le2-g4.Sf3.0-0, h4-h5
with 10!/8!/2!=45 possibilities
The same is true for Black:
a5.Ta6-e6-e5.e6.De7-d6-a6, b5.Lb7
Without white/black interactions there would be
45*45=2025 games
But castling is prevented, when [Pb7] is still on b7 and Da6 controls f1, i.e., in the games ending with
8... Da6 9.0-0?? b5 10.h5 Lb7
which happens in eight games (1.h4, 2.h4, ..., 8.h4)
2025 - 8 = 2017 (2017-08-31)
more ...
comment
Keywords: Non-Unique Proof Game, Path enumeration (year), Capture-free, Castling
Genre: Retro, Mathematics
FEN: 1n2kbnr/1bpp1ppp/q3p3/pp2r1NP/4P1B1/5N2/PPPP1PP1/R1BQ1RK1
Input: A.Buchanan, 2017-08-30
Last update: A.Buchanan, 2021-10-25 more...
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A.Buchanan (1)