# The riddle of the necklace

I will take this opportunity to point out that the fact that my riddles are well known does not imply that everyone knows the answers.

The correct answers of some of the most popular have never been published and as far as I know they have not been discovered. I will demonstrate this point by presenting the "Riddle of the necklace" that I published several years ago and that makes every person who reads it believe that they can easily solve it. However, I don't remember that anyone has found the right answer.

It is based on a daily business transaction and aims to demonstrate to what extent ordinary people are wrong when it comes to performing a task that requires a minimum of mathematical ability or knowledge. It is devoid of any kind of trap or subterfuge and there is no mysterious "missing link" in it.

It was proposed to the main jewelers and goldsmiths of New York who said they would not hire any seller who could not solve such a simple transaction and yet none of them gave the right answer.

A lady bought twelve pieces of chain as shown around the illustration and wanted to make a closed necklace of 100 links. The jeweler said it would cost 15 cents to cut and join a small link and 20 cents to cut and join a large link. The question is to say how much the lady must pay to have her necklace made. That's it and it's a nice problem for young people.

#### Solution

When responding to this riddle of the necklace, it can be said that any jeweler like ninety-nine percent of mathematicians will say that the best way would be to open the twelve small links at the end of nine of the twelve pieces, a fact that would cost \$ 1.80.

However, the correct answer involves opening the ten links of the two pieces of five links located on the left and right sides to join the remaining 10 pieces of chain available.

Opening and crimping those links to make a closed collar would cost \$ 1.70, which is the cheapest possible solution.