Mathimagics wrote:David P Bird wrote:I devised it in 2007 in response to a knitting group who wanted a design for an Afghan pattern. It has the properties:

a) that the 9 cells in the same position in each box hold complete 1-9 digit sets for the left and right digits.

b) that every left hand digit is paired once with every right hand digit .

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Thanks David.

Your properties are essentially the definition of "Orthogonal Sudoku".

If we label the two Sudoku grids A and B (ie grid A = left digits, grid B = right digits), then we find that grid A has NTV = 243 , from which we can obtain 67,158 different orthogonal pairs (Grid B) one of which will (with suitable labelling) will match your example.

Given the high NTV count, I assume that grid A has automorphs. Can anyone confirm?

I can see that your grids have property b) but they don't have property a)

1 2 3 | 4 5 6 | 7 8 9

4 8 7 | 9 2 1 | 5 6 3

9 6 5 | 3 7 8 | 1 2 4

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5 3 8 | 2 4 9 | 6 1 7

2 4 9 | 6 1 7 | 8 3 5

7 1 6 | 8 3 5 | 9 4 2

-------------------------

8 7 2 | 5 6 3 | 4 9 1

3 9 1 | 7 8 4 | 2 5 6

6 5 4 | 1 9 2 | 3 7 8

This is your grid from Jan 2nd where I have underlined instances where the same digit occurs in the same positions in different boxes, for example, (3)b1r1c3 and (3)b8r1c3. However, it may be possible to transform it to avoid this.

The Afghan A & B grids have 36 automorphs and B is a morph of A (but I guess that follows automatically).

If you use Excel, I can provide you with a custom worksheet function to canonicalise a solution string (using the Anchor-5 system) to give you automorph counts.

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