Can't Follow The Program's Logic

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Can't Follow The Program's Logic

Postby Yogi » Sat Apr 30, 2016 9:08 am

Can someone help me understand what this program is telling me? Here's the position:
000700029029386705007209008862907530053068972790523860300692157216875493975030286
The Solver (from RCBroughton) then said
86. X-Chain on candidate 1 at r1c3=r2c1 - r5c1=r5c4 - r9c4=r9c6
86a. Removed candidate 1 from r1c6

I simply can't follow it. For my own interest I worked the puzzle through with r1c6=1 and this did lead to an inconsistency.
So the program is right. I just can't follow the reasoning.
Yogi
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Re: Can't Follow The Program's Logic

Postby Leren » Sat Apr 30, 2016 9:48 am

Code: Select all
*--------------------------------------------------------------*
| 56    348  a148    | 7     145   4-1    | 36    2     9      |
|b14    2     9      | 3     8     6      | 7     14    5      |
| 56    34    7      | 2     145   9      | 36    14    8      |
|--------------------+--------------------+--------------------|
| 8     6     2      | 9     14    7      | 5     3     14     |
|c14    5     3      |d14    6     8      | 9     7     2      |
| 7     9     14     | 5     2     3      | 8     6     14     |
|--------------------+--------------------+--------------------|
| 3     48    48     | 6     9     2      | 1     5     7      |
| 2     1     6      | 8     7     5      | 4     9     3      |
| 9     7     5      |e14    3    f14     | 2     8     6      |
*--------------------------------------------------------------*

OK this is the X chain position marked in cells abcdef.

Assume r1c3 is not 1.

Then r2c1 must be 1 (only 2 1's in Box 1)

so r5c1 must not be 1

so r5c4 must be 1 (only 2 1's in Row 5)

so r9c4 must not be 1

so r9c6 must be 1 (only 2 1's in Row 9).

Now, if you start by assuming r9c6 is not 1, then you can follow a similar chain of reasoning by following the cells in the reverse order (fedbca), and you'll find that r1c3 must be 1.

The net result of all this is that at least one of cells a and f (r1c3 and r9c6) must be 1. They might both be 1 but they can't both be not 1.

Since r1c6 sees both of these cells it can't be 1.

The standard notation for this is (1) r1c3 = r2c1 - r5c1 = r5c4 - r9c4 = (1) r9c6 => - 1 r1c6.

This is an example of what is called an alternating inference chain (AIC for short), which is just a set of alternating True/False inferences.

Here are some links to sites that discuss this topic.

http://www.sudokuwiki.org/Alternating_Inference_Chains

http://hodoku.sourceforge.net/en/tech_chains.php#x

Hope this helps, Leren
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Re: Can't Follow The Program's Logic

Postby Yogi » Sun May 01, 2016 12:24 am

Very good. You have explained it: r1c6 sees both ends of the 6-link chain running from r1c3 to r9c6, and one of those must be 1. Therefore r1c6 cannot be 1 and must be 4.
STTE! (A new term I have recently learned.)
I suppose if I had focussed more on the word CHAIN and looked at the 6 locations mentioned I should have got it. My mind was sent in the wrong direction by the use of = which I read as "The same as," and - which I took to be "Not the same as." Why can't computers talk Human?
Thanx.
Yogi
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Re: Can't Follow The Program's Logic

Postby Leren » Sun May 01, 2016 1:17 am

stte stands for Singles to the End - a cascade of naked or hidden singles until the puzzle is fully solved.

The = sign in chain notation stands for a Strong link. A Strong link exists between a and b when a being False implies b is True.

Similarly a - sign stands for a Weak link. A Weak link exists between a and b when a being True implies b is False.

Leren
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Re: Can't Follow The Program's Logic

Postby Yogi » Sun May 01, 2016 2:15 am

Gotcha
Yogi
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