My wife and I just returned from a wonderful cruise along the Yangtze River. Although I could have logged onto the Internet from the ship, residual sanity prevented me from working through our vacation. However, the idea of buying things to take on a trip reminded me of a little charmer of a puzzle. Like many of the puzzles I present here, this one stumped me for a few moments until I had an “a-ha” experience. Then the answer came quickly.

Assume you are packing to go on a trip and at the last minute you realize that you need a few more things. What to do? It’s late at night and the stores are not open. You hop in the car and rush down to your nearby 7-11 store. The night clerk does not look wide awake, but he rings up the four items, and you are surprised when the total is $7.11 - just like the store. You check the bill carefully because you do not trust the clerk.

“That’s odd,” you say, “The sum of my four items is the same as your logo.” You grab your things and start to leave when the clerk calmly says, “Yeah, and the product of the four prices is the same.” That stops you cold, but a quick calculation on your wristwatch data bank confirms what the clerk said. The sum of the four prices and the product of the four prices are both the same! You leave somewhat humbled about your ability to judge other humans.

What were the values of the four items? Note: in the state where this puzzle occurred, there is no sales tax.

I could tell you the wrong path I started down to solve this puzzle, but the answer quickly becomes obvious if you see the wrong path, so I will not give any more clues (although this is a clue in a way…).

This puzzle is simply that - a puzzle. It has nothing to do with decision theory. Solving it won’t be of any practical value whatsoever. Like my trip to China, it is meant solely for fun.

Enjoy.

For those who wish to delve further into decision theory without wading through a lot of equations, I have posted a tutorial on elementary decision theory. It shows examples of faulty physicians’ diagnoses (important for those considering surgery) and how to evaluate anti-terrorist activities (important for everyone). That tutorial can be found here.

Tags: sherman deforest, puzzle, decision theory, yangtze river, 7-11, sales tax