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

1 - P1259074

Suomen Tehtäväniekat 1993

(2+7) C+

ser-h=11. How many solutions?

**Kauko Väisänen**

Arto PuusaArto Puusa

Suomen Tehtäväniekat 1993

(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.

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.

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.

**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...

Show statistic for complete result. Show search result faster by using ids.

https://pdb.dieschwalbe.de/search.jsp?expression=PROBID%3D%27P1259074%27

The problems of this query have been registered by the following contributors:

A.Buchanan (1)
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