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Old 11-24-2005, 07:01 PM
Cosimo Cosimo is offline
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Join Date: Jul 2003
Location: Austin, TX
Posts: 199
Default Re: Need help with a Sudoku

Take these points under consideration:
__x ___ __h
aax qq_ s__
__x __q sh_

___ ___ ___
_B_ _F_ ___
b__ ___ ___

_C_ _E_ ___
cc_ ___ _gg
dd_ ___ ___

The g squares are leaf squares. Although choosing them first (randomly) can force the rest of the puzzle, they only interact with one other square each, and again that other square has 8 and 9 as options (the h squares here). Hence, ignore the g squares. Tricks like this help you narrow down where you need to look. Similarly, the h, s, and x squares don't affect anywhere else, ie they are forced by the q squares.

So, to conclude, the puzzle will have to be solved by the interactions among the bottom-left 6x6 subgrid (and maybe aa and qqq).

An out is suggested by the common two-value pairs in the leftmost two columns.

The a squares have to be 3 or 7. Note that there is no interaction with these two squares and anything else in the row; it is leaf-ish in that a forced restriction somewhere else is going to be easier to find. They are not true leaves because the 3 and 7 occur in different places elsewhere in the columns. Compare the gg and hh squares: the g squares are perfectly determined soley by the h squares. There's no internal restrictions or interactions there. Here, a interacts with b, c, and d squares.

Now look at the sets aa, Bb, Ccc, and dd. For one column, where there's a 7 in one of the c squares, there's a 3 in a, an 8 in d, and a 4 in b. This reduces to: in a column where there's a 7 in a c square, there's a 4 in the respective b square. I'll call this the c7b4 column restriction.

Now take BFEC. An 8 needs to be in either B or F, and a 3 in F or E, and a 1 in E or C. So BFEC is either 831x or x831. This 'forcing loop' puts restrictions on the Bb and Ccc squares.

Next step, in white: <font color="white">combine the forced loop with the c7b4 column restriction: if BFEC is 831x, then C has to be 7, which contradicts the column restriction. Hence BFEC is x831.</font>
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