Puzzle | Chain Link Puzzle

You have 5 separate chain segments, each made up of 3 links.

• Breaking open a link costs $1.
• Closing (welding) an open link costs $3.
• You may only connect segments by breaking and welding links.

Connect all 5 segments into one long continuous open chain (ends remain free, not joined into a loop) while spending less than $15.

What is the minimum cost to connect all segments into a single open-ended chain?

Check if you were right - full answer with solution below.

Solution: 

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

• Take chain 1 and break open all three links: 1 x 3 = $3. 
• Take one open link to connect chain 2 and 3: $3. 
• Take another open link to connect chain 3 and 4: $3. 
• Take the third open link to connect chain 4 and 5: $3. 

⁛ Now you have one long chain ready in only $12.