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1 problem(s) found in 5136 milliseconds (displaying 1 problem(s)). [A='Heinonen' AND K='Path enumeration'] [download as LaTeX]

1 - P1258968
Unto Heinonen
Suomen Tehtäväniekat 12/1993
P1258968
(5+3) C+
ser-h#14. How many solutions?
1. h5 2. h4 3. h3 4. h2 5. h1=D 6. Dg1 7. Da7 8. h5 9. h4 10. h3 11. h2 12. h1=D 13. Dhg1 14. Dgb6 Sb4#
is one example.
play all play one stop play next play all
The first and last moves are forced, but in between there is a 6+6 queue.
Catalan numbers C_n = (2n)!/(n!(n+1)!).
Here there are C_6 = (12!/(6!7!) = 132 solutions.
Problem 1: Suomen Tehtäväniekat Christmas solving contest Dec 1993.
paul: Unique solution with Relay Chess. (2021-08-16)
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comment
Keywords: Path enumeration (Catalan), Seriesmover
Genre: Mathematics, Fairies
Computer test: Gustav 4.1 d gives 132 lines in solution file
FEN: 8/1N5p/k1P4p/8/8/3N4/8/1K3B2
Input: A.Buchanan, 2013-01-11
Last update: Olaf Jenkner, 2021-08-16 more...
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A.Buchanan (1)