So I was staring at the 2nd Pentopia of the WPC 2013 practise test written by Ko Okamoto thinking how I ended up with multiple solutions. I reread the rules at least four times and came up empty. How odd, I thought, since I have solved a few Pentopias before. I looked at the first Pentopia of the set, which was straightforward, and found nothing wrong.
A fifth look at the rules saw me emphasizing the last sentence: pentominoes may be rotated but NOT reflected. There we go. The puzzle solved itself.
There’s nothing upsetting about forbidding reflection, but it leaves an empty room for a flexibility-loving nut like me. When I construct puzzles using polyminoes I have Blokus pieces handy to quickly prove uniqueness. Blokus players will no doubt have the habit of twisting and reflecting polyminoes in their heads to optimize those nasty land-grabbing moves.
Which leads me to my point: why disallow reflection of pentominoes in puzzles?
Reflection affects 2 tetrominoes, namely the L (or J) and S (or Z), and thankfully most tetromino puzzles forgive reflection. Imagine a LITS where S and Z are two different pieces; there goes a boatload of beautiful deductions.
However when we’re dealing with pentominoes, 7 of 12 pieces form a “different” shape when they are flipped over. This reduces the number of possible orientations rather significantly. Puzzles with this rule will be easier since there will be less possible positions. Not only for solvers, but this also cut authors some slack when constructing the said puzzle.
Have I been solving pentopias all these years without ever knowing is rule?
A quick check at Puzzle Para Site, since one would associate Pentopias with Bram De Laat, revealed that reflections are in fact allowed.
Maybe there are certain puzzle types where not allowing reflection is better. But for now, I’ll have my seven extra orientations, thanks.