MathDB
2021 Combo Div 1 P5

Source:

March 2, 2021
combinatorics

Problem Statement

There are exactly 7 possible tetrominos (groups of 4 connected squares in a grid):
https://cdn.discordapp.com/attachments/813077401265242143/816189385859006474/tetris.png
Daniel has a 2×202102 \times 20210 rectangle and wants to tile the interior with tetrominos without overlaps, pieces sticking out, or extra pieces left over. Note that you are allowed to rotate tetrominos but not reflect them.
For how many multisets of tetrominos (ie. an ordered tuple of how many of each tile he has) is it possible to exactly tile his 2×202102\times20210 rectangle?
Proposed by Dilhan Salgado