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## Usenet Newsgroups : rec.puzzles Hall of Fame

The rec.puzzles Hall of Fame is a compilation of over 500 of the most popular puzzles that have been posted and discussed in the rec.puzzles newsgroup. In most cases a detailed solution has been provided.

Many of these puzzles also appear in Braingle's own collection.

 rec.puzzles Newsgroup FAQ Hall of Fame alt.brain.teasers Newsgroup FAQ
Categories : decision : envelope.p

Someone has prepared two envelopes containing money.  One contains twice as
much money as the other.  You have decided to pick one envelope, but then the
following argument occurs to you:  Suppose my chosen envelope contains \$X,
then the other envelope either contains \$X/2 or \$2X.  Both cases are
equally likely, so my expectation if I take the other envelope is
.5 * \$X/2 + .5 * \$2X = \$1.25X, which is higher than my current \$X, so I
should change my mind and take the other envelope.  But then I can apply the
argument all over again.  Something is wrong here!  Where did I go wrong?

In a variant of this problem, you are allowed to peek into the envelope
you chose before finally settling on it.  Suppose that when you peek you
see \$100.  Should you switch now?

Solution

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