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A few years ago Warren Buffett started offering $1 billion to anyone who could correctly predict the winner of every game in the NCAA men's basketball tournament. A 64 team (we won't count the first four play-in games) single-elimination tournament bracket like "March Madness" has 2^63 possible bracket combination, putting the odds of correctly predicting a perfect bracket around 1 in 92 quadrillion.

But what if I don't want to leave this up to chance or skill? If I wanted to submit all 2^63 possible brackets to ensure that I submitted a winner, how improbable is this? I see two limiting factors - computational time and storage space, although I might argue that this is possible.

My question is two-fold:

  1. Given current computing limitations, how long would it take to compute all possible brackets? Particularly, how long would it take to compute one bracket, and how quickly could the fastest computer compute them all?

  2. How much space would storing these brackets take, and is it a feasible amount of storage?

For 2, my guess is that it's a lot of data, but it's feasible. A bracket can be represented by 63 bits, each bit representing a game in the tournament and the 1 or 0 signifying whether the high or low seed won. Thus we have 2^63 brackets, each at 7.875 bytes each, for a total of roughly 72.6 exabytes of data. Given that Google is estimated to have between 10-15 exabytes of data, this is an absurd amount of data but not out of the realm of storage possibility.

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The rate-limiting factor is the cost of submitting each of those $2^{63}$ combinations. Since submitting a combination probably requires (at minimum) opening a network connection and sending the combination to a remote server, you can generate combinations a lot faster than you can submit them. Similarly, the cost of storing the submissions is probably negligible compared to the time it takes to submit them all.

In particular, if it takes one second to submit a proposed combination, it will take you $2^{63}$ seconds to submit all $2^{63}$ of them. That's about 21 times the age of the universe. If it takes you one millisecond to submit a single combination, it will take you $2^{63}/1000$ seconds to submit them all -- that's about 300 million years. Obviously, not possible within your lifetime.

Also, note that the contest rules specified a maximum of one entry per person, as well as a maximum of 15 million submissions (not 15 million per person; 15 million total -- once there have been 15 million combinations submitted, the contest closes). Consequently, your proposed strategy simply wasn't possible. The creators weren't dumb: presumably, they thought of that and made sure it wouldn't happen.

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