This set of T-shapes was devised by Jim Kerley who asked whether 1,2,3, or 4 sets would tile a rectangle (they will probably not, search nearly complete, tilings can be found for five sets or higher).

No overlaps/gaps, and you can flip the Ts if you think that will help. I rate this as surprisingly difficult and recommend you try it by hand before moving to a computer solution. I'm not saying you won't find a tiling by hand, but I would be impressed.

The sets of T-shapes can be discerned from this valiant attempt to tile a rectangle with six sets. Each set has area 80 squares, being of sizes 4,5,6,7,8,6,8,10,12,14.

[![59-partial with six sets][1]][1]


  [1]: https://i.sstatic.net/WtvUvswX.png