Henry Ernest Dudeney/Modern Puzzles/212 - A Chain Puzzle

by : $212$

 * A Chain Puzzle
 * A man has $80$ links of old chain in $13$ fragments, as shown in the diagram.


 * Dudeney-Modern-Puzzles-212.png


 * It will cost him $1 \oldpence$ to open a link and $2 \oldpence$ to weld one together again.
 * What is the lowest price it must cost him to join all the pieces together so as to form an endless chain?


 * A new chain will cost him $3 \shillings$ (that is, $36 \oldpence$)
 * What is the cheapest method of procedure?
 * Remember that the small and large links must run alternately.