Puzzle Details

You have five pieces of chain, each consisting of three links. You want to make one long chain of these five pieces. Breaking open a link costs 1 dollar, and welding an open link costs 3 dollars. Is it possible to make one long chain of the five pieces, if you have just 15 dollars?

Solution

The most straightforward approach would be to break a link on the end of each of the four chains, and then reattach the link to the back of the next chain. This would cost you \$16 for the four links that were broken and resealed.

But you can actually do it for \$12!
Instead of breaking a link in each chain, break all three links in one of the chains and then use those three links to attach the remaining four chains together.

Let us name the chains 1, 2, 3, 4, and 5 each having three links.

Take chain 1 and break open all three links: 1×3=3 Dollars.
Take one open link to connect chains 2 and 3:  3 Dollars.
Take another open link to connect chains 3 and 4:  3 Dollars
Take the third open link to connect chains 4 and 5:  3 Dollars.

Now you have one long chain ready for only 12 Dollars

by following this logical approach we can create a longer chain using 5 smaller chains with 3 links each in investing just 12 dollars.