Testwiki:Reference desk/Archives/Mathematics/2013 July 25

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July 25

two digit sudoku and its answer

please arrange a two digit sudoku with numbers and also its answer — Preceding unsigned comment added by 202.83.50.219 (talk) 10:56, 25 July 2013 (UTC)

There is a general procedure for producing an $n^2\times n^2$ sudoku. In the first row, list the numbers 1 thru $n^2$ in order. For the next n rows, cyclically permute the first row by blocks of n. Then for row n+1 cyclically permute the first n slots of the first row, the second n slots of the first row, etc. For row n+2, do this to the second row, and so on. For instance, applying this procedure for a 9x9 sudoku gives

123456789

456789123

789123456

231564897

564897231

897231564

312645978

645978312

978312645

It's left as an exercise how to do this, eg, for whatever two digit size you had in mind (16x16, 25x25, 81x81). (Note: this clearly will not generate all possible suduko's, even if you are allowed to change the labels, but you just asked for one.) Sławomir Biały (talk) 12:24, 25 July 2013 (UTC)

To be fair, that's "only" a solution. The question how many squares are needed to make a sudoku unique hasn't been attacked above.

Wildly WP:ORing, I'd say it looks like that par tof the problem would be NP (complexity).

I guess a two-digit sudoku is one with 10 to 99 different symbols, and if you want numbers, those would be two digits per square. That would be, 3 < n < 10. (n=10 is ok if, contravening usual sudoku conventions, all combinations from 00 to 99 are used.) - ¡Ouch! (^{hurt me} / _{more pain}) 16:36, 27 July 2013 (UTC)