Problem

Source: Ukrainian National Math Olympiad 4th round

Tags: combinatorics unsolved, combinatorics



There are $100$ cards with numbers from $1$ to $100$ on the table.Andriy and Nick took the same number of cards in a way such that the following condition holds:if Andriy has a card with a number $n$ then Nick has a card with a number $2n+2$.What is the maximal number of cards that could be taken by the two guys?