I am making a program that generates $3$ random polyominoes of size $x \le n$ (referring to the number of squares in the shape). Each polyomino fits within a space: $k \times k$ ($k=6$ in my case).
I am trying to determine the maximum value of $n$ where all 3 polyominoes are guaranteed to fit in a space of size $L \times M$. For this problem, the pieces can be rotated, but not mirrored.
(for my current case: $L=M=8$)
In this example $n=10$ with the worst case $x = n$ for all 3 pieces. As you can see, there exists at least 1 solution.
