|
Some years ago my friend Robert Reid conceived the idea of what he calls "cover up puzzles". His first design required you to place three U pentominoes on the table in such a way that you could cover them up with five straight trominoes. This puzzle was simultaneously designed by at least one other designer.
Subsequently Robert has designed several more cover up puzzles. Two years ago, inspired by his idea, I had the idea of coating the surface of a pentacube with the five tetrominoes. See here for more details.
Recently I was thinking about expanding this idea and came up at the following. Most of the pentacubes just have 22 unit surfaces, although two have only 20. By taking three Pentacubes and joining them, it is possible to create a three-dimensional object, which has 60 units surfaces. This seems an ideal shape for covering with the 12 flexible pentominoes. I also wondered if it would be possible to take three identical planar pentacubes, combine them as described above, then cover the outside with 12 copies of the same planar pentominoes.
Diagram 1 it shows a possible three-dimensional object, made from three F pentacubes. they are joined in such a way as to have 60 square units on their surface. Diagram 2 shows the same pieces connected in a way which is incorrect, by way of the the total number of units being less than 60. Diagram 3 shows the three pieces joined in a planar fashion.
|
