## September 30th, 2005

### Puzzle 18: To Each Their Own

With the great popularity of Polyominous and my own Seeking Syren here, I figured it'd be worth presenting more variations on polyomino-divvying. I discovered this design in issue 100, the only one I own, of Puzzle Communication Nikoli; given that each letter in the grid needs its own polyomino, each character has its own congruence class, and Nikoli's title for the puzzle - NIKOJI - strikes me as rather pompous, I figure my title is a perfect fit. This design presents a first among my LiveJournal puzzles: no numbers! In many ways, this is a cipher Polyominous.

The grid on the left is an unsolved To Each Their Own puzzle; the grid on the right is the unique solution to that same puzzle, rendered in indigo. The cyan line segments are a solving aid I employ and are not part of the solution.

The object is to take the given grid and divide it into polyominoes such that each has exactly one given letter in it and that given any two such polyominoes arbitrarily, they otherwise match exactly - in size, shape, orientation, and the position of the letter within - if and only if the letters they contain match each other.

Still a simple puzzle, but the list is still here:

1) Except for the outside border, the puzzle grid shows only the corners of the cells of the grid. To solve the puzzle, draw in the needed borders between cells so as to divide the grid up into sections following the remaining rules.
2) Every section the grid is split up into must have one letter in it - no more, no less.
3) If two sections have identical letters in them, then the sections they are in must be identical to each other. They must have matching cell counts; their shapes must be identical to each other; they must be lined up identically (if one section has to be rotated, flipped over, or both to look like the other, they do NOT match); they even need to have those matching letters in matching spots within.
4) If two sections do NOT have identical letters in them, then they must NOT be otherwise identical. At least one of the following must be true in that case: one has more cells than the other; their shapes don't match; one would have to be rotated, flipped over, or both in order to get the two to look like each other; their letters are not in matching cells with respect to the borders of the sections.

It is just as important to not use the word 'different' in puzzle instructions as it is to not use the word 'same'. Ambiguity is NOT a good thing in puzzle instructions. But if you're thinking "same letter = same section, different letter = different section", what you're thinking is hopefully correct. Look up at the sample solution: the two A-regions match each other, and the two E-regions match each other, but if you take an A-region and an E-region, they do not match... since although they have the same size, shape, and orientation, the letter is in the left-hand cell of the E-regions and the right-hand cell of the A-regions. I hope that quells any lingering doubts as to what I'm asking for, but if not - or if you can't seem to figure out how to approach this - here's the standard walkthrough:

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I probably could have made a tougher one than the one below, but I felt like being cute with this first one. It's easy, but it's fun. Let me know what you think of this design in the comments; email me your solution if you finish, and maybe I'll reward you and maybe I won't.

On deck: two more designs I haven't presented here yet. - ZM