The New Sudoku Players' Forum

by **rds2301** » Sat Jan 14, 2006 4:05 pm

what is the difference between forcing chains and guessing? i.e assuming one of a pair and seeing if it leads to a contradiciton

by **MCC** » Sat Jan 14, 2006 4:17 pm

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by **Carcul** » Sat Jan 14, 2006 4:17 pm

Hi rds2301.

The difference is in pattern recognition: forcing chains involve strong and weak links, which can be drawn to make a Bilocation-Bivalue plot and then nice loops (double implication forcing chains) can be identified to make deductions. This does not happen in Trial and Error or in Guessing.

Regards, Carcul

by **Myth Jellies** » Sat Jan 14, 2006 8:11 pm

Spotting an ab-cell, which sees a bc-cell, which sees a ca-cell is not guessing. Neither is the realization that you can then eliminate the 'a's from all other cells that see both the ab-cell and the ca-cell. This would be represented in the posts as something like

Code: Select all: [r1c1]-a-[r1c9]-b-[r3c8]-c-[r3c3]-a-[r1c1] => (r1c1 <> a) aX-cell ab-cell bc-cell ca-cell aX-cell

Note that the aX-cell is just the cell that sees both the ab-cell and the ca-cell that I described above. The symbolic chain representation may appear to indicate that a guess was involved, but that does not have to be the case. Often, depending on the type of chain, the meat of the pattern you searched for is in between the two endpoints. The endpoints are the same cell which closes the loop.

That is just one of the simplest forcing chains. It can have more links, and there are various kinds of links and more complicated chains with different realizations that can be made from them, but they all should work without any guesses involved.

by **tso** » Sat Jan 14, 2006 9:33 pm

If I hand you a 12 inch loop of rope that has a large knot in it and ask you to find the knot -- you will see the knot and point it out. Is this guessing?

If I hand you a 100 foot loop of rope that has a large knot in it -- and the lights are out -- you will pass the rope through your hands one way or the other until you reach the knot. Is this guessing? Does it matter which way you passed the rope though your hands? Did you *know* that you would find the knot?