# Need help on proceding a paper about estimating numbers of sudoku

I was reading a paper that I found via spiked math (http://spikedmath.com/comics/424-the-numbers-quiz-solutions.png): http://www.afjarvis.staff.shef.ac.uk/sudoku/sudoku.pdf.

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It would help if you say what you don't understand. The rearrangement strategy is used before in the paper, trying to reduce the number of configurations that need to be counted. – Ross Millikan Jun 24 '11 at 4:40
I can't see where the "2051 possible B2/B3 pairs" comes from. – Covi Jun 25 '11 at 5:04

For every assignment of the first three rows, we assign a canonical form by first applying the unique permutation on the digits $1,\ldots,9$ such that the first square is $1,2,3;4,5,6;7,8,9$, then rearranging the other 6 columns in some canonical way (see details in the paper). Canonicalization doesn't change the number of completed sudokus.