April 2026 Problem of the Month

A man goes into a jewelry store and inquires about the cost of several pieces of jewelry.   The shopkeeper says:

"The amethyst necklace and the diamond brooch together cost $2700.
The diamond brooch and the ruby bracelet cost $4300.
The ruby bracelet and the sapphire earrings cost $3100.
The sapphire earrings and the emerald pin cost $2900.
The emerald pin and the topaz ring cost $2300."

The customer says, "I'll take the piece that costs $1300."

Which item did he buy?

Solution to the Problem:

Here is the solution:

The customer bought the sapphire earrings.

If any other piece of jewelry cost $1300, it would cause the price of either the amethyst necklace or the topaz ring to be less than zero.

Click here for Dr. Kishan's excellent explanation