Question

A subset S of {1,2,…,n} is said to be packed if whenever i,j∈S the number ⌊(i+j)/2⌋ is also in S. Determine how many subsets of {1,2,…,25} are packed.

Details and assumptions
i and j need not be distinct. If i=j is in the set, then clearly so is ⌊(i+j)2⌋

Answer 1

http://www.google.com/search?q=brilliant+A+subset+S+of+%7B1%2C2%2C%E2%80%A6%2Cn%7D+is+said+to+be+packed+if+whenever+i%2Cj%E2%88%88S&oq=brilliant+A+subset+S+of+%7B1%2C2%2C%E2%80%A6%2Cn%7D+is+said+to+be+packed+if+whenever+i%2Cj%E2%88%88S&aqs=chrome.0.57j0.4007j0&sourceid=chrome&ie=UTF-8

Answer 2

Yup it's cheating