IMO 1988 LL NET68

Let S be the set of all sequences {ai | 1 \leqi \leq7, ai = 0 or 1}.

imolonglistmathematicsolympiad

IMO 1988 LL NET68

Origin: NET

Problem

Let S be the set of all sequences {ai | 1 \leqi \leq7, ai = 0 or 1}. The distance between two elements {ai} and {bi} of S is defined as 7 i=1 |ai −bi|. Let T be a subset of S in which any two elements have a distance apart greater than or equal to 3. Prove that T contains at most 16 elements. Give an example of such a subset with 16 elements.