A blacksmith, a chain and seven days of work: the most elegant solution is not always the most obvious.
The seven links
Riddle statement
A blacksmith agrees to pay a laborer with a small gold chain made up of 7 closed links.
The deal is this: for 7 days, he must deliver exactly one gold link per day.
You can take back links already delivered to make change, but you want to make as few cuts as possible in the chain.
How many cuts do you need at least?
Show solution
Solution
The key is to create pieces that, combined with returns, allow you to represent any quantity from 1 to 7.
The ideal pieces are sizes 1, 2 and 4: with them any number between 1 and 7 can be formed without the need for more.
This is achieved with a single cut, opening the third link counted from one end. The chain is converted into three pieces:
- a loose link (1)
- a section of 2 links
- a section of 4 links
From there, the daily payment works like this:
day 1: delivery 1 day 2: recover 1 and deliver 2 day 3: delivery plus 1 day 4: recover 1 and 2, deliver 4 day 5: delivery plus 1 day 6: recover 1 and deliver 2 day 7: delivery plus 1