Did you remedy it? The magic of the Borromean rings | Arithmetic

Earlier right this moment I set the next puzzle, impressed by the Borromean rings (left), that are three interlocking loops with the property that once you take away any certainly one of them, the opposite two are not linked. Within the puzzle the whole lot falls aside when one aspect is eliminated.

Smash the image

The image beneath reveals the traditional method to grasp an image on a wall with two nails. The 2 nails give one another back-up: if one fails, the image will nonetheless grasp (wonkily) on the opposite nail.

Pic on wall

Are you able to consider a method to grasp an image on a wall utilizing string and two nails, such that if both of the nails fails (and the opposite one doesn’t) then the image will fall to the ground?


There are a number of methods to unravel this puzzle. A technique is the Borromean rings. Simply as they’re three interconnected rings that collapse when one is eliminated, the puzzle entails three interconnected parts (two nails and a chunk of string), and when one is eliminated (the nail) the opposite two are not linked. Our activity is thus to work out precisely how the puzzle fashions the rings. Right here’s the way you may go about it. Make a set of Borromean rings with two plastic rings and a chunk of string as beneath:

x2.12 Picture on Wall A2 v3

Subsequent, separate the rings as if they’re nails on the wall.

X2.13 Picture on wall A3 v4

The best way the string loops between the rings is the answer we’re after, offered beneath. If both of the ‘nails’ are eliminated, we all know that the string and the opposite nail can’t be linked, and thus the portray will crash to the ground.

X2.14 Picture on wall A4

There are different options too, resembling:

X2.11 Picture on Wall A1

You might have most popular a physics-style reply that makes use of drive and friction. It might be attainable to stay the nails in so shut to one another that they clasp a string that holds up a portray. On this case, eradicating both nail will trigger the portray to drop.

In case you are on this space, the paper Image-hanging Puzzles by E. Demaine, M. Demaine, Y. Minsky, J. Mitchell, R. Rivest and M. Patrascu has many extra examples and touchers on deeper concepts in topology and laptop science.


A 3D model of the Borromean rings (left) is the emblem of the Worldwide Mathematical Union , which is having its centennial on September 27 and 28. The schedule options talks by 17 of the world’s prime mathematicians and shall be broadcast stay.

I set a puzzle right here each two weeks on a Monday. I’m at all times on the look-out for nice puzzles. If you want to recommend one, electronic mail me.

I’m the writer of a number of books of puzzles, most lately the Language Lover’s Puzzle Ebook. I additionally give college talks about maths and puzzles (restrictions permitting). In case your college is please get in contact.

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