One number is visible and another remains hidden. You may ask for no further information, but the value you have seen may already reveal more than it seems.
The Other Number
Riddle statement
Two real numbers are generated independently, each chosen uniformly from the interval \([0,1]\).
One of the two numbers is then selected at random and shown to you. The other remains hidden.
After seeing the visible number, you must make one of two claims:
- “The hidden number is greater.”
- “The hidden number is smaller.”
You may ask no additional questions.
Can you succeed with probability greater than \(1/2\)?
Find the optimal strategy and prove the greatest possible probability of success.
The two numbers are equal with probability zero, so ties need not be considered.