The Riddler

An old Riddler Express problem:

Submit a whole number between 1 and 1,000,000,000. I’ll then take all those numbers and find the average submission. Whoever submits the number closest to ⅔ of the mean of all of the submitted numbers wins.

So if we get a bunch of random submissions, then the mean of those guesses would be 500,000,000. 2/3 of that would be 333,333,333. But if enough people use that logic, then that would be the mean and 2/3 of that would be 222,222,222.


Repeatedly taking 2/3 of 500 million looks like this graph, or this equation:

scaled down to make it legible. Anyway, it heads toward zero, so my guess is one.