# 2019 AMC 10C Problems/Problem 23

### Problem

Bernado has an infinite amount of red, blue, orange, pink, yellow, purple, and black blocks. He puts them in the 2 by 2019 grid such that adjacent blocks are of different colors. What is the hundreds digit of the number of ways he can put the blocks in?

### Solution

There are choices to choose the colors for first section. Without loss of generality, assume that the first group of two is Red-Blue. There are ways to choose the colors of the next section, but we would over-count by 5 if the new top and bottom are the same.Thus, there are only distinct choices for the second group of vertical blocks. Now we just have to find the hundreds digit of . Now we can do some binomial expansions to find the hundreds digit of that number: Thus, the answer is .

## Video Solution

~IceMatrix