The Yin/Yang problem is to find a holeless polyhex that can be tiled by each of two different pentahexes, leaving a single hole shaped like the other. It was inspired by the corresponding problem of Jenard Cabilao for pentominoes, which you may see (in Flemish) at KSO Glorieux's Pentomino site.
Here I show minimal known Yin/Yang solutions for every pair of pentahexes. If you find a smaller solution or solve an unsolved case, please write.
5A-5C | 5A-5D | 5A-5E | 5A-5F | 5A-5H | 5A-5I |
---|---|---|---|---|---|
5A-5J | 5A-5K | 5A-5L | 5A-5N | 5A-5P | 5A-5Q |
5A-5R | 5A-5S | 5A-5T | 5A-5U | 5A-5V | |
5A-5W | 5A-5X | 5A-5Y | 5A-5Z | ||
5C-5D | 5C-5E | 5C-5F | 5C-5H | 5C-5I | |
5C-5J | 5C-5K | 5C-5L | 5C-5N | 5C-5P | 5C-5Q |
5C-5R | 5C-5S | 5C-5T | 5C-5U | 5C-5V | 5C-5W |
5C-5X | 5C-5Y | 5C-5Z | 5D-5E | 5D-5F | 5D-5H |
5D-5I | 5D-5J | 5D-5K | 5D-5L | 5D-5N | 5D-5P |
5D-5Q | 5D-5R | 5D-5S | 5D-5T | 5D-5U | 5D-5V |
5D-5W | 5D-5X | 5D-5Y | 5D-5Z | 5E-5F | 5E-5H |
5E-5I | 5E-5J | 5E-5K | 5E-5L | 5E-5N | 5E-5P |
5E-5Q | 5E-5R | 5E-5S | 5E-5T | 5E-5U | 5E-5V |
5E-5W | 5E-5X | 5E-5Y | 5E-5Z | 5F-5H | 5F-5I |
5F-5J | 5F-5K | 5F-5L | 5F-5N | 5F-5P | 5F-5Q |
5F-5R | 5F-5S | 5F-5T | 5F-5U | 5F-5V | 5F-5W |
5F-5X | 5F-5Y | 5F-5Z | 5H-5I | 5H-5J | 5H-5K |
5H-5L | 5H-5N | 5H-5P | 5H-5Q | 5H-5R | 5H-5S |
5H-5T | 5H-5U | 5H-5V | 5H-5W | 5H-5X | 5H-5Y |
5H-5Z | 5I-5J | 5I-5K | 5I-5L | 5I-5N | 5I-5P |
5I-5Q | 5I-5R | 5I-5S | 5I-5T | 5I-5U | |
5I-5V | 5I-5W | 5I-5X | 5I-5Y | 5I-5Z | 5J-5K |
5J-5L | 5J-5N | 5J-5P | 5J-5Q | 5J-5R | 5J-5S |
5J-5T | 5J-5U | 5J-5V | 5J-5W | 5J-5X | 5J-5Y |
5J-5Z | 5K-5L | 5K-5N | 5K-5P | 5K-5Q | 5K-5R |
5K-5S | 5K-5T | 5K-5U | 5K-5V | 5K-5W | 5K-5X |
5K-5Y | 5K-5Z | 5L-5N | 5L-5P | 5L-5Q | 5L-5R |
5L-5S | 5L-5T | 5L-5U | 5L-5V | 5L-5W | 5L-5X |
5L-5Y | 5L-5Z | 5N-5P | 5N-5Q | 5N-5R | 5N-5S |
5N-5T | 5N-5U | 5N-5V | 5N-5W | 5N-5X | 5N-5Y |
5N-5Z | 5P-5Q | 5P-5R | 5P-5S | 5P-5T | 5P-5U |
5P-5V | 5P-5W | 5P-5X | 5P-5Y | 5P-5Z | 5Q-5R |
5Q-5S | 5Q-5T | 5Q-5U | 5Q-5V | 5Q-5W | 5Q-5X |
5Q-5Y | 5Q-5Z | 5R-5S | 5R-5T | 5R-5U | 5R-5V |
5R-5W | 5R-5X | 5R-5Y | 5R-5Z | 5S-5T | 5S-5U |
5S-5V | 5S-5W | 5S-5X | 5S-5Y | 5S-5Z | 5T-5U |
5T-5V | 5T-5W | 5T-5X | 5T-5Y | 5T-5Z | 5U-5V |
5U-5W | 5U-5X | 5U-5Y | 5U-5Z | 5V-5W | 5V-5X |
5V-5Y | 5V-5Z | 5W-5X | 5W-5Y | 5W-5Z | 5X-5Y |
5X-5Z | 5Y-5Z | ||||
Last revised 2013-08-01.