Did you solve it? The magic of the Borromean rings

The Borromean rings (left) inspired me to create the following puzzle. When one of the elements is removed, everything in the puzzle falls apart.
Smash the picture

Below is an example of how to hang a picture with two nails. Two nails support each other: If one of them fails, the picture will still hang (wonkily), on the other.

Is there a way to hang pictures on a wall with string and two nails? If one nail fails, the other doesn't, the picture will go to the ground.


This puzzle can be solved in many ways. Borromean rings are one way to solve this puzzle. The puzzle is made up of three interconnected rings, which fall apart when one of them is removed. It also includes two nails and a piece string. When one nail is removed, the other two pieces are no longer connected. The puzzle's model of the rings is therefore our task. Here's how to do it. You can make a Borromean set with two plastic rings, a piece string and one of the other rings.

Next, remove the rings and place them on the wall.

Below is the solution. It's the way that the string loops between each ring. We know that the string cannot be connected if one of the nails is removed. The painting will then fall to the ground.

Other solutions exist, too.

Perhaps you prefer a physics-style solution that uses force and friction. You might be able to put the nails so close together that they hold a string that holds up the painting. The painting will drop if one nail is removed.

This paper, Picture-hanging Puzzles by E. Demaine and M. Demaine, Y. Minsky and J. Mitchell, R. Rivest, and M. Patrascu, has more information and touches on deep ideas in topology, computer science, and other areas.

The International Mathematical Union logo (left) shows a 3D model of the Borromean rings. It celebrates its centennial this September 27 and 28. The schedule includes talks by 17 top mathematicians around the globe and will be broadcast live.

Every Monday, I create a new puzzle. I am always looking for new puzzles. Send me an email if you have any suggestions.

I am the author of many puzzle books, including the Language Lovers Puzzle book. If you are interested, I can also speak to schools about mathematics and puzzles (restrictions permitting). Please contact me if your school is interested.