Any two elements have distance apart greater than or equal 3
Source: IMO LongList 1988, Netherlands 2, Problem 57 of ILL
November 3, 2005
combinatorics unsolvedcombinatorics
Problem Statement
is the set of all sequences \{a_i| 1 \leq i \leq 7, a_i \equal{} 0 \text{ or } 1\}. The distance between two elements and of is defined as
\sum^7_{i \equal{} 1} |a_i \minus{} b_i|.
is a subset of in which any two elements have a distance apart greater than or equal to 3. Prove that contains at most 16 elements. Give an example of such a subset with 16 elements.