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Is the mathematical principle of nine chains not clear enough?
Nine chains is an example of a typical recursive problem. There are only three basic laws:

The outermost ring is always free to put on or take off the straight lock handle;

The outermost two rings can always put on or take off the straight lock handle freely together;

If any of the other rings A can be freely put on or taken off the straight lock handle except the outermost two rings, it must be ensured that only one ring A is put on the straight lock handle outside.

According to this rule, you can completely untie the nine chains, or you can restore the nine chains that have been untied.