2014 Fall Team #1
Source:
March 26, 2022
combinatorics
Problem Statement
Suppose we have a hexagonal grid in the shape of a hexagon of side length as shown at left. Define a “chunk” to be four tiles, two of which are adjacent to the other three, and the other two of which are adjacent to just two of the others. The three possible rotations of these are shown at right.
https://cdn.artofproblemsolving.com/attachments/a/7/147d8aa2c149918ab855db1e945d389433446a.png
In how many ways can we choose a chunk from the grid?