A Tetrahedron That Always Lands on the Same Side
How many times has the following scenario happened to you?
You playing with a tetrahedron, one of those strange geometrical objects whose defining characteristic is that it has four flat sides that are all shaped like triangles, when you suddenly drop it. As it falls, you starting placing mental bets on which of the four sides will land on. Will the side you pick win?
If you’re like most people, the answer to the question of how many times this scenario has happeend to you is almost never. Not only do you not run into random tetrahedrons to play with, the game of dropping one to see which side will be on top is not a very fun one to play. The only way to make it interesting is to gamble on the outcome, which makes it a bad dice game, but one with better odds. Instead of a one in six chance of getting it right, you have a one in four chance.
But if you’re going to put money down to play this incredibly boring game with the equivalent of a four-sided die, would you really want to lose on average three times out of every four drops?
Of course not! If you want to win all the time, you’re going to have to figure out a way to transform your tetrahedron into a loaded die, one that always comes up the way you want it to. Sure, that’s cheating, but if money is on the line in playing this game, you want to be the one collecting it from the rubes you might be playing with. How can you rig the game so your tetrahedron always comes out with your winning side on top?
Good news, everyone! Mathematicians have figured out how you can always beat this game. Stand Up Maths’ Matt Parker breaks the news in the following video…
And there you have it, a loaded tetrahedron that you can use like a loaded die to always win bets related to which side will it land on if you drop it!
For more information about how this achievement was realized, check out Quanta Magazine‘s article on the discovery of the monostable tetrahedron!
Source: https://politicalcalculations.blogspot.com/2025/09/a-tetrahedron-that-always-lands-on-same.html
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