problems/cmo03.txt

*** Problem Statement ***

Let $n$ be a positive integer. There are $n$ red cards and $n$ blue cards. Initially, every red card has the real number $0$ written on it, and every blue card has the real number $1$ written on it.
An operation consists of selecting one red card and one blue card such that the number $x$ on the red card is strictly less than the number $y$ on the blue card, erasing both numbers, and replacing them both with the average $\frac{x+y}{2}$.
Find the minimum positive integer $n$ such that it is possible, using a finite sequence of these operations, to make the sum of the numbers on the $n$ red cards strictly greater than 100.