Puzzle: Chain 1
Critically acclaimed rapper Drake recently bought some ridiculous fashion statement in the form of a large golden chain. Unfortunately, this golden chain broke into 9 pieces, each consisting of series of individual links of lengths \(\{1, 2, 3, \dots, 8, 9\}\). He would like to get the chain repaired and his jeweler informs him that sawing and soldering a link back together costs $80 but that he would fix the entire chain for $700. What is the lowest cost for which the 45-link chain can be repaired?
Answer
To join 9 pieces into a single chain, you need 8 joins (each join reduces the number of pieces by 1). Each join costs $80, so the total cost is:
Thus, 640 is less than the $700 flat repair fee and is the minimum cost.
Notes and comments
Comment 1: The cost is not $720 because the chain is simply joined end-to-end without molding it into a circle requiring an extra $80.