Question 250635
I have a program that solves this problem. It produces 2,339 unique solutions
using a 6 by 10 rectangle, a 5 by 12 rectangle with 1,010 solutions, a 4 by 15 rectangle with 1,424 solutions and a 3 by 20 rectangle with 2 solutions.
I don't think you'd be interested in the c++ program that does the work.
Besides I can't find a way to draw these rectangles with all the pieces in this system.