MathDB

4

Part of 2022 Thailand Online MO

Problems(1)

Remove 1011 signs from 2022 signs and the remaning can be any color

Source: 2022 Thailand Online MO P4

4/4/2022
There are 20222022 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 10111011 whose each term is either red or blue, Auto can always remove 10111011 signs from the line so that the remaining 10111011 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.
combinatorics