Science & Tech

Games, Cheats, and Puzzles

Terence Tao

Lesson time 07:43 min

Terence has always been drawn to imaginary scenarios that operate within a set of guidelines or rules. He demonstrates a puzzle and how it can actually provide a life-saving solution, and he converts a math puzzle into tic-tac-toe.

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Topics include: Games, Cheats, and Puzzles The Counterfeit Coin Puzzle Gaming Cheat!


[MUSIC PLAYING] - As a kid, I loved computer games, logic puzzles. I think I was always drawn to artificial scenarios where the rules were very clear and simple. There was a certain number of moves you could do. There was a sense of a right answer and a wrong answer. Certainly there's the thrill of solving them, especially if they have somehow fought against you. You get a sense that they're almost alive. And the same is true for a really good puzzle or a good game. I'd like to talk about how a toy puzzle can lead to a very practical application, which had nothing to do with the original puzzle, at least at first glance. [MUSIC PLAYING] So there's a classical puzzle, almost 100 years old, called the Counterfeit Coin Puzzle. You're given 12 coins, let's say, gold coins, let's say. And they're all identical, except for one, which is counterfeit. And the counterfeit coin is either slightly heavier or slightly lighter than the other coins. You don't know which coin is the counterfeit one, and you don't know whether it's heavier or lighter. And your task is to work out which coin is counterfeit. And the only tool you're given is a balance scale. And you can put some coins on one side of the scale, some coins on the other. And you can see whether the coins are evenly matched or whether one is heavier, one is lighter. But the catch is, you're only allowed to use the weighing scale three times. So if there's 12 coins, you can't weigh each coin separately. You're only allowed three weighings. This is a purely mathematical puzzle. There's no conceivable practical situation where you have to determine a kind of a coin and you have this very limited number of weighings. So the solution for this counterfeit coin problem is quite complicated. And we'll include a full solution in the class guide. It uses a mathematical object called a matrix. And the techniques we use to solve this problem actually turn out to also be useful to solve a very different problem that I was involved in, actually, about 10, 15 years ago, which was that of MRI scanning. So an MRI machine scans your organs for things like tumors or other anomalous objects. But the problem is that these machines are somewhat slow. And for certain patients, like young children, they may not be able to stay still for enough time for the scan to actually work. So there was a question. Could you figure out whether there was a tumor using fewer measurements than the traditional MRI scan? And this problem turns out to mathematically very similar to the coin weighing problem. For instance, there is a way to solve the coin weighing problem using a field of mathematics called linear algebra. And maybe we will discuss this more in the written notes. And the same type of mathematics is also used to solve the compressed sensing problem. You put your body inside this machine, they measure these magnetic fields, and with enough measurements they can reconstruct a...

About the Instructor

A MacArthur Fellow and Fields Medal winner, Terence Tao, PhD, was studying university-level math by age 9. Now the “Mozart of Math” is breaking down his approach to everyday problem-solving—without complex equations or formulas. Learn how to deconstruct challenges, use storytelling as a tool, and discover solutions, whether you’re trying to level up in a computer game or just catch your plane on time.

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Terence Tao

World-renowned mathematician Dr. Terence Tao teaches you his approach to everyday problem-solving—without complex equations or formulas.

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