Enclosing Unique Pentominoes
Here is an unsolved question that is similar to the topic discussed in my first article. In that previous article I was trying to use all twelve pentominoes to properly enclose as many copies of pentomino-shaped cavity as possible (where each hole is the same shaped pentomino).What if we try to arrange the pieces to properly enclose pento-shaped cavities where each hole is different? How many pento-holes can we enclose? Here is an example showing five different cavities:
And here is another such example:
Is it possible to make six uniquely shaped cavities? It certainly seems that there are enough extra unit volumes floating around to do it, but I have not yet been able to make such a configuration.
- Eric Harshbarger, 24 Jun 2020