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.pngDaniel has a 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 rectangle?Proposed by Dilhan Salgado