Am I cheating?

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Am I cheating?

Postby Glenn100 » Tue Feb 13, 2018 7:41 pm

Please look at Fig 1. lt is much like like any row you will quite often in a puzzle. While this is a row, the same thing I am to ask about can be found in any house.

Fig 1
| 9 26 256 | 4 7 3 | 258 1 28 |

Notice that there are (4) 2's in this row...two of which are in bi-valves. Namely, 2-6 in A2 and 2-8 in A9.

Now let's try what I have been doing to solve which is the cell location for the 2 in this row. See Fig 2

Fig 2

| 9 +26 -256 | 4 7 3 | -258 1 -28 |

You see I have made the 2 A2 a black plus and all of the others a black minus 2.
Now we know that if my assumption of the 2 in A2 is correct the the 2 in A9 cannot be a 2.
So if that is the case look at Fig 3

Fig 3

| 9 -26 -256 | 4 7 3 | -258 1 +28 |

You can now see that I have put a plus red 2 in A9. and the rest of the 2's in that row a minus red. Now if you look at Fig 2 and compare to Fig 3 that there are both a minus red and a minus black in A3 and A7. This indicates that the the 2's in those cells can be deleted.
Whoopee it worked which indicates either the 2 in in A2 or A9 is the proper candidate for that row. And the 2's in A3 and A7 can be deleted.
Looks like winner doesn't it? But hold on.

Remember, I ASSUMED that the one the 2's in A2 and A9 were going to be correct. If neither of those 2' are the correct candidate for that row, the correct candidate will be found in either A3 or A7. But which one. In one of those two cells you will NOT be able to delete the 2 which means that is the correct candidate for the 2. So A2 will become 6 and A9 will become an 8. cell A3 will have the 2 removed from it.

I have been doing the essentially the same in other puzzles using both red and black. And those don't require using the (double whammy) as above

So when I see a row like depicted here, I know i will find the candidate for that row. I use "Super Sudoku" to keep track of the candidates in each cell. Also, I know all of Scanraids basic algorithms plus about 8 others and always reduce all puzzles as much as I can without resulting to the plus/minus that is depicted above. To me it is not guessing but what do you think? Is this valid or guessing and why?
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Joined: 29 October 2013

Re: Am I cheating?

Postby 200e200w » Tue Feb 13, 2018 8:04 pm

Hi, Glenn!
What you have descripted, is a pure guessing. You are cheating this way, because you do not know which combination of cells 2 and 9 is true, 2-8, 6-2 or 6-8. The latter one does not make any eliminations for 2 in this house, so at least one of the eliminations of 2s in cells 3 and 7 is true, but this does not mean that both eliminations are true! That's why you are cheating this way.

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Joined: 20 January 2018

Re: Am I cheating?

Postby David P Bird » Tue Feb 13, 2018 8:54 pm

Glen, there are six ways of picking two cells:
Code: Select all
    A2  A3  A6  A8
    x   x   .   .       
    x   .   x   .
    x   .   .   x
    .   x   x   .
    .   x   .   x
    .   .   x   x
Say A2 is the true cell. If we test each of these six options, 3 times out of 6 you will eliminate it.
You are therefore guessing

David P Bird
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Location: Middle England

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