Although this isn't new, I just came across it (perhaps again) and was so enchanted that I wanted to share it.
Generate but don't look at three random numbers. (Have someone ensure that they are distinct. There is no constraint on the range.) Look at the first two. You are now able to guess with a better than 50% chance of being right whether the first number is larger than the unseen third. I like this almost as much as the Monte Hall problem. *-- Russ *
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