An explanation of the 2-variable sudoku thing.

OK, a couple people asked about 2-variable sudoku. I think this is something that has a lot of other names. The one that’s ringing a vague bell with me is a Euler square.

So I’ll explain.

In standard sudoku, your job is to make sure that every box in a square is filled in with numbers between 1 and 9, but no numbers can repeat in any given row or column. You’re given some starting numbers, almost always placed symmetrically, and you have to figure out the rest. There are lots of non-standard sudoku as well, but that’s basically it.

In two-variable sudoku, you aren’t just putting in 1 through 9, nine times each. Each digit also has nine colors, and the colors may not repeat within a row or column either.

It’s probably easier to reduce it to a 4×4 square instead of 9×9. Let’s say you have 16 cards, labeled A1, A2, A3, A4, B1, B2, B3, B4, C1, C2, C3, C4, D1, D2, D3, and D4. Your job is to arrange them so that no column or row repeats a letter OR a number.

Here’s one solution:

A1 B2 C3 D4
D3 C4 B1 A2
B4 A3 D2 C1
C2 D1 A4 B3

Here’s the weird thing. You can do it with a 1×1 square (duh), but not a 2×2 square. You can do it with 3×3, 4×4, and 5×5. You can NOT do it with 6×6. But you can then do it with any size square from 7×7 on up.

That’s what I meant about 36 being kind of cool, mathematically. You can’t make a Euler square with 36 two-variable options.

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