MathDB
Combinatorics

Source: Danube Mathematical Competition,Seniors #2

October 29, 2016
combinatorics

Problem Statement

A bank has a set S of codes formed only with 0 and 1,each one with length n.Two codes are 'friends' if they are different on only one position.We know that each code has exactly k 'friends'.Prove that: 1)S has an even number of elements 2)S contains at least 2k2^k codes