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

hint: consecutive. This is a brilliant question please do not give full answer.