Onesided Polarized Pentominoes


Here are the 35 pieces packed in five 5x7 rectangles.


We can look for combined 1, 3 and 5-fold models of the pentominoes. For all but the I-pento the construction is possible. For the I-pento I think, we can't get a solution, but perhaps I'm wrong. With some sets of rectangles it should be also possible to make 5-fold replicas of the heptominoes.


Starting with a 15x15 square we can choose the position of two 5x5 square holes and try to solve the puzzle. Which positions are promising?


Using a little house as the basic cell you get a physical representation of the pieces. Is it possible to color the pieces with five colors so that you can make a solution whith five same colored rectangles, and another solution where pieces of the same color don't touch?