"Y Hexomino" has a shape as shown in the picture.
What is the maximum number of Y Hexomino that can be placed on a $13\times 13$ chessboard, where each Hexomino does not overlap?
From the diagram below, we can place a maximum of 24 Hexominoes. However, how can we prove that no more can be placed? In the general case, it seems that we can place a maximum of $6n^2$ hexominoes on a $(6n+1)\times (6n+1)$ chessboard , using a similar method to the $13\times 13$ case. How can we demonstrate the validity of this conjecture? Thanks in advance.
