Remove 1011 signs from 2022 signs and the remaning can be any color
Source: 2022 Thailand Online MO P4
April 4, 2022
combinatorics
Problem Statement
There are signs arranged in a straight line. Mark tasks Auto to color each sign with either red or blue with the following condition: for any given sequence of length whose each term is either red or blue, Auto can always remove signs from the line so that the remaining signs match the given color sequence without changing the order. Determine the number of ways Auto can color the signs to satisfy Mark's condition.