GamesNovatory/Devices/Hand-held/The Chain

Origin of the Game
How can one open only 2 links of a 23-link chain so as to produce all the values from 1 to 23 ?

chain2-23

The Device
There are 2 kinds of chains commercially available -
     1. Plastic chains are found in most "dollar" stores,
          in which any link can be easily opened and removed from the chain.
     2. There are also metal "U-links", mostly used on sailboats to connect guy wires,
          in which the pin which screws the "U" tight can be removed and the link opened.
               These come in different sizes and can be found in hardware stores.
          These links have the advantage of remaining open
               and not closing automatically like the plastic links.

Mathematics
To see the Mathematics of the chain

chain1-7

Pedagogy
With small children, it is preferable to start with the small 7-link chain,
in which only 1 is opened,
and proceed by trial and error.
The length of the first section (2 links) and the position of the open link (the 3rd)
can be clearly seen and later imagined for more elaborate examples.

Once the 7-link chain is well understood,,
working with the 23-link chain should not be too difficult.