one piece of string, ribbon or similar, which may form a closed loop or which may have other pieces like balls fixed to its end.
one or several pieces of stiff wire
sometimes additional pieces like wooden ball through which the string is threaded.
One can distinguish three subgroups of wire-and-string puzzles:
Closed string subgroup: Here the pieces of string consists of one closed loop. Usually the string has to be disentangled from the wire.
Unclosed loose string subgroup: Here the pieces of string is not closed, and is not attached to the wire. In this case the ends of the string are fitted with a ball, cube or similar which stops the string from slipping out too easily. Usually the string has to be disentangled from the wire. Sometimes other tasks have to be completed instead, such as shifting a ring or ball from one end of the string to another end.
Unclosed fixed string subgroup: Here the pieces of string is not closed, but is somewhere on its length attached to the wire. Obviously in these puzzles the task is not to disentangle the string from the wire. One possible task may be to shift a ring or ball from one end of the string to another end.
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