Chinese rings

Classic version with 4 rings, but because of the cat figure it is counted among those with 5 rings.

This version has one more branch.

The Chinese rings are a conundrum , the aim of which is to free a long wire loop from the connected rings. Another variant (also Baguenaudier in the French and English-speaking areas ) has fixed rings that cannot move in relation to one another, which are mounted on a board and from which a loop of cord has to be freed.

history

Steward Culin, an American ethnographer , found out that this puzzle goes back to a Chinese general Hung Ming (181–235 AD).

solution

The solution requires a sequential "freeing" and re-threading of individual rings and, analogous to the towers of Hanoi, works like a binary Gray code . To solve a puzzle with rings you need a maximum of movements (depending on the initial state) . ${\displaystyle n}$ ${\displaystyle {\begin{cases}{\frac {2^{n+1}-2}{3}},&{\text{wenn }}n{\text{ gerade,}}\\{\frac {2^{n+1}-1}{3}},&{\text{wenn }}n{\text{ ungerade.}}\end{cases}}}$

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  Puzzle in its initial state ...

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  ... while loosening ...

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  ... and solved.

Web links

• Interactive solver
• Many variations of this puzzle
• Topological view of the puzzle (PDF; 208 kB)

Individual evidence

1. ↑ Eric Weisstein: Baguenaudier . In: MathWorld (English).
2. ↑ http://www.cs.brandeis.edu/~storer/JimPuzzles/ZPAGES/zzzChineseRings.html
3. ↑ http://oeis.org/A026644