Hypothesis Tests · Superchallenge problem

A measurement has standard deviation 10 on each of two occasions, and a subject's two measurements have correlation $0.8$. A paired study measures 25 subjects twice and uses the mean difference. An unpaired study instead measures $n$ different subjects on occasion 1 and $n$ other subjects on occasion 2 and uses the difference of means. What is the smallest $n$ for which the unpaired study's standard error is no larger than the paired study's?