The “Hexed” puzzle is also called the pentominoes puzzle. “Penta” is the from the Greek language and means five. Each pentomino is formed by joining 5 squares edge to edge. Another word of similar origin is “domino” which is 2 squares joined edge to edge.
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The 12 pieces are given names that relate to letters of the alphabet. One way to remember the names is to think of 5 letters in the word “Philipino” followed by the last 7 letters of the alphabet. “Philipino” is changed to be spelled “FILIPINO”, the “O” is dropped, and the duplicates removed giving FILPN and TUVWXYZ. Below is a picture of the mapping. Note that some of the pieces need to be rotated to look like the corresponding letters.
Back in 1970 I wrote computer programs to find all of the solutions to the problem. My first program was written in assembly language on an IBM 360/75 while I was a student at Caltech. It took 45 minutes of CPU time on one of the fastest computers of that era to find all of the solutions. The program was created by using an IBM 026 key punch machine to punch little rectangular holds in 80 column punch cards that were 7.375 inches wide and 3.25 inches high. The solutions were printed using the limited character set on the mainframe line printer. I used the underscore ( _ ) and the vertical bar (|) to draw the solutions. It wasn’t perfect, but it was usable. As printer capabilities increased I have since written programs using the PCL printer language to display the solutions. The output from a LaserJet printer is far superior to the old line printer version.
Note that in order to remove rotations and reflections from the solutions I displayed only solutions that have the V character oriented as it is shown in the illustration above. The following 4 solutions are really all the same solution reflected horizontally and vertically.