SQUARES WANTED
I and sanket were playing monololy a game in which you have 3 envelopes, each containing a uniformly random amount
of money between 0 and 1000 dollars. (That is, for any real 0 ≤ a < b ≤ 1000, the probability that the
amount of money in a given envelope is between a and b is b−a
1000 .) At any step, you take an envelope and
look at its contents. You may choose either to keep the envelope, at which point you finish, or discard
it and repeat the process with one less envelope. If you play to optimize your expected winnings, your
expected winnings will be E. What is bEc, the greatest integer less than or equal to E?
The answer is 695.
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