The New Sudoku Players' Forum

[vidarino]

I have been experimenting with unique patterns lately, and their use in nice loops. When working with a type 5 Unique Rectangle I noticed an interesting shortcut.

Consider this grid, with a type 5 UR in R14C12.

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     13*   135*     8 |      15     27     67 |       9     46    246
     12      6      4 |      18      3      9 |       5      7     28
      9     57     27 |     568    268      4 |       1      3    268
----------------------+-----------------------+----------------------
    135*    13*     9 |      68     68      2 |       7     45     34
    567      8     67 |       4      1      3 |       2     56      9
      4      2     36 |       7      9      5 |       8      1     36
----------------------+-----------------------+----------------------
   3678     37   1367 |       9     67     18 |       4      2      5
     28      4     12 |       3      5     18 |       6      9      7
     67      9      5 |       2      4     67 |       3      8      1


Now, since one of the 5s in the UR must be true, they can be considered as forming a strong link between their respective corners. Also, note that the 1s form a conjugate pair in both column 2 and row 4, so we have strong links in those units as well.

That means that we have a tiny discontinuous Nice Loop:

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R4C2=1=R4C1=5=R1C2=1=R4C2  =>  R4C2=1

This handy conclusion can be reasoned as follows; If R4C2 was NOT 1, the corners R1C2 and R4C1 would be one instead (they were the only 1s left in the column and row, respectively). This would eliminate the 5s from the corners, and result in a deadly pattern (i.e. we could swap the 1s and 3s in the corners and still have a valid grid).

So, there you have it. Not superfantastically easy to spot, but not too hard either. And it can often lead to a swift placement of a couple of numbers. One at least.

Vidar

[ronk]

That means that we have a tiny discontinuous Nice Loop:

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R4C2=1=R4C1=5=R1C2=1=R4C2  =>  R4C2=1

Yes, I think that's as 'tiny' as they get. I noted a very similar deduction here. That one had a 2s x-wing overlaying the UR(24) (type 2C or type 5).

The tiniest continuous Nice Loop would be naked (or hidden) pair.

Ron

[vidarino]

Hrm, seems I need to check ronk's posting history before publishing any more "discoveries". ;-)

Anyway, as a curiosity related to the one above, here's another tiny loop that uses an Almost Unique Rectangle, but with an acrobatic mid-air candidate-change;

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      3      6     14 |      14      7      9 |       2      8      5
      7     29      8 |       3     24      5 |     469     46      1
     49     12      5 |       8      6     12 |     479      3    479
----------------------+-----------------------+----------------------
     28      5      9 |     147      3    246 |      18    467    478
     28      4     67 |       5    129    126 |       3    167    789
      1      3     67 |      47     49      8 |    4679      5      2
----------------------+-----------------------+----------------------
      6      7    134 |       9      5     34 |      18      2     48
     49    189      2 |       6     18     47 |       5    147      3
      5     18     34 |       2    148   1347 |      47      9      6

The AUR with 18 in R89C25 provides us with a strong link R8C2=9|4=R9C5, yielding the loop:

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R8C5=8=R8C2=9|4=R9C5=8=R8C5  ->  R8C5 = 8

Vidar

[ronk]

The AUR with 18 in R89C25 provides us with a strong link R8C2=9|4=R9C5, yielding the loop:

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R8C5=8=R8C2=9|4=R9C5=8=R8C5  ->  R8C5 = 8

Nice one.

Hrm, seems I need to check ronk's posting history before publishing any more "discoveries". ;-)

Not any more, as you've probably already hit my only good ones.

Ron

[Neunmalneun]

I understood your first example (AUR 13) since R4C2 = 3 forces a perfect UR.

But I don't get this nice loop in your second example. Why does the AUR (18) lead to R8C5 = 8? Couldn't R8C5 be 1 (with R8C2 = 1, R9C2=8, R9C5 = 4) without forming a UR pattern?

[ravel]

Couldn't R8C5 be 1 (with R8C2 = 1, R9C2=8, R9C5 = 4) without forming a UR pattern?

Then you would have 2 1's in row 8. The 1 in R8C5 would force R8C2 and R9C5 to be 8.

[vidarino]

But I don't get this nice loop in your second example. Why does the AUR (18) lead to R8C5 = 8? Couldn't R8C5 be 1 (with R8C2 = 1, R9C2=8, R9C5 = 4) without forming a UR pattern?

(Edit: I seem to have brainfarted earlier.)

There are only two 8s in C5. If R8C5=1 and R9C5=4 you have eliminated them both.

Vidar

[Neunmalneun]

Thanks a lot. Now I see the deduction. Best regards