5

Alice takes two envelopes and puts some number of dollar bills in each one. These can be any positive whole numbers (we're putting realism aside), but they cannot be the same number.

Bob chooses one envelope and looks at its contents, but not those of the other envelope. Bob then decides which envelope to keep. Devise a strategy by which Bob has a greater than $1/2$ chance of keeping the envelope with more money. This must be true no matter what distinct numbers Alice chose.

(This is a classic that many of you are probably familiar with, but I didn't find it on the site. If you've seen it, I'd kindly request that you wait before answering to give others a chance.)

xnor
  • 26,756
  • 4
  • 85
  • 144
  • (... putting realism aside) the bills are massless and infinitely thin? In other words, there is no way to physically measure or guess at the contents of an envelop without looking inside? – Dacio Apr 15 '15 at 22:21
  • @IanMacDonald Good find, that's totally a duplicate. – xnor Apr 15 '15 at 22:29
  • @xnor, it wasn't me that found the duplicate, I was just the first to cast a vote. – Ian MacDonald Apr 16 '15 at 01:24
  • @Dacio: Alice puts seven 5-unit bills in one envelope, and three 20-unit bills in the other. – jscs Apr 16 '15 at 02:49

0 Answers0