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steven0461 comments on A Request for Open Problems - Less Wrong
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In the Gaussian case, you can do better than (A, B) but the demonstration of that fact won't smack you in the face they way it does in the case of the uniform distribution.
One thing you can do in the uniform case is shorten the interval to at most length 1/2. Not sure if that's face-smacking enough.
You can do better than that. If the distance between the two data points is 7/4, you can shrink the 100% confidence interval to 1/4, etc. (The extreme case is as the distance between the two data points approaches 2, your 100% confidence interval approaches size zero.)
EDIT: whoops, I was stupid. Corrected 3/4 to 7/4 and 1 to 2. There, now it should be right