Here are 3 simple tiling puzzles. A 5x5 square is tiled with 5 pieces, one a single sub square, the other 4 each made of 6 sub squares. The single piece has been omitted so the tiled square has a missing piece.
The four pieces of puzzle 1 are all the same. It can only be solved if the missing square is at the center. Not hard, it has a pleasing four fold symmetry.
Puzzle 2 has 4 different pieces. It can only be solved if the missing piece is at the center and is a bit harder.
Puzzle 3 also has four different pieces. It has multiple solutions; the missing piece can be a corner one, at the middle of an edge, one position diagonally moved in from a corner, or at the center. It can take a few minutes to find all four solutions.
OpenSCAD construction and viewing programs are included.
The puzzles print quickly at draft resolution. To reduce confusion it is probably best to print them in different colors.
While working on these puzzles I received a letter from D Moews that described a general search for the above tiling problem. Files included with the letter summarized and listed the results. Puzzle 1 is line 4 in answers-by-counts, puzzle 2 is line 40, and puzzle 3 line 2412.
There are 2472 sets of four 6 piece tiles, plus a single sub square, which will tile the 5x5 square. The image below shows the first 8 sets of possible tiling pieces.
An edited version of D Moews's letter, "Tilings of a 5x5 square.txt", and the summary lists are included. The lists can be used to construct more puzzles; directions for how to do so are included in make_puzzles.scad.