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1 problem(s) found in 673 milliseconds (displaying 1 problem(s)). [PROBID='P1259074'] [download as LaTeX]

1 - P1259074
Kauko Väisänen
Arto Puusa

Suomen Tehtäväniekat 1993
P1259074
(2+7) C+
ser-h=11. How many solutions?
1. Tf3 2. Tf5 3. Th3 4. Thf3 5. h4 6. h3 7. Th5 8. T3f5 9. Th4 10. Tfh5 11. g5 Lxh2= is one example.
play all play one stop play next play all
There are 5 pieces moving in a loop over 5 squares. Viewed as a cycle, there are just two configurations: XXX00 & XX0X0. XXX00 can only move to XX0X0, while XX0X0 can move to either configuration. The repeated application of the adjacency matrix:
(0 1)
(1 1)
means that the number of ways to reach any position is a fibonacci number.
We need the 9th fibonacci number (1,1,2,3,5,...), so there are 34 solutions.
Problem 5: Suomen Tehtäväniekat Christmas solving contest Dec 1993.
A.Buchanan: The published proof did not mention Fibonacci. Search k="path:fib" here in PDB to see some other situations where he appears. (2013-01-13)
comment
Keywords: Seriesmover, Minimal, Path enumeration (Fibonacci)
Genre: Mathematics, Fairies
Computer test: C+ Jacobi v0.7.5 ~6000s
FEN: 8/6p1/7p/4B2p/4K1kr/7r/7p/8
Input: A.Buchanan, 2013-01-11
Last update: A.Buchanan, 2022-06-01 more...
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A.Buchanan (1)