ELI5: Explain Like I'm 5

Prouhet–Tarry–Escott problem

Have you ever counted how many marbles you have and how many buckets you can put them in? Maybe you can put 2 marbles in each bucket and you have 6 marbles, so you need 3 buckets.

The Prouhet-Tarry-Escott problem is a tricky math problem that asks you to find how many buckets you need to put some marbles in. But the trick is that you have to use lots of different amounts of marbles and lots of different sized buckets.

For example, let's say you have 3 marbles and you want to put them in buckets that can hold 2 marbles each. You would need 2 buckets because you can't put 3 marbles in just 1 bucket.

Now, imagine you have 3 different amounts of marbles: 1, 3, and 9. And you have 3 different sized buckets: 2, 3, and 5 marbles. How many buckets do you need to put all of the marbles in?

That's what the Prouhet-Tarry-Escott problem wants you to figure out. And it's not as easy as just adding up all the marbles and dividing by the bucket size. You have to use a special math formula to solve it.

So, basically, the Prouhet-Tarry-Escott problem is a tricky math puzzle that asks you to figure out how many buckets you need to put different amounts of marbles in different sized buckets. But don't worry, even big grown-up mathematicians have trouble with it sometimes!