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An Extended Form of Medusa Coloring
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Sat Feb 02, 2008 12:38 am    Post subject: Reply with quote

I only went two days this time. Can an inference be made based on an assumption of true in two or more cells? Consider these two cells in a line:

23g 2g34

Can we say that if 2g3g are both true, then the 4 can be inferred, thus creating a wrap? Seems too easy.

Or this:

38g 35g 158

Can we infer the 1 assuming that the 5g8g are both true?
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Sat Feb 02, 2008 7:02 am    Post subject: Reply with quote

Marty R. wrote:
Can an inference be made based on an assumption of true in two or more cells?

Yes, but...

In your first example, I don't see that there is any inference about the <4> in those two cells. We only know that the <4> is false if G is true (since in that case the cell must be <2>). But, that isn't very helpful. I certainly can't see a "wrap."

However, if that <4> were strongly linked to another <4> that already shared a cell with a "g" value, then you would have a wrap (since G would eliminate all <4>s in that house).

In the second example, we can infer that the <1> is "g", but not that it is true. In other words, if G is true, then the third cell must be <1>, hence, it can be colored "g".

I hope that is clear.
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Sat Feb 02, 2008 4:16 pm    Post subject: Reply with quote

A,

Thanks, I hope for the last time.

I wasn't thinking very clearly when I presented my first example. How can you infer a cell is "x" if you assume it's "y'"? Embarassed
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Thu Feb 21, 2008 4:29 pm    Post subject: Reply with quote

Consider the following partial grid with made-up numbers just to illustrate the point:

Code:
+-------+-------+-----------+
| . . . | . . . | 49g .   . |
| . . . | . . . | 139 .   . |
| . . . | . . . | 13  .   . |
+-------+-------+-----------+
| . . . | . . . | 17  .   . |
| . . . | . . . | .   69g . |
| . . . | . . . | .   .   . |
+-------+-------+-----------+
| . . . | . . . | .   .   . |
| . . . | . . . | .   .   . |
| . . . | . . . | .   .   . |
+-------+-------+-----------+

The 9g in box 6 has inferred the 9g in box 3. The latter 9g infers a naked 13 pair just below it. Is this a legitimate trap whereby r4c7 can be solved for 7? I'm used to my traps coming from little r's and g's.

Or is all we can do is mark the 7 with a "g"?

(First question in 20 days). Very Happy
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Fri Feb 22, 2008 12:02 am    Post subject: Reply with quote

Marty wrote:
Is this a legitimate trap whereby r4c7 can be solved for 7? ... Or is all we can do is mark the 7 with a "g"?

All you can do is mark the 7 with a "g". The <1> can only be removed if it can "see" a red <1> somewhere.

[Edit to remove unnecessary comment.]
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Fri Feb 22, 2008 1:19 am    Post subject: Reply with quote

As always, thanks.
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Mon Mar 31, 2008 12:35 am    Post subject: Reply with quote

Code:
+-------+-------+---------+
| . . . | . . . | . .   . |
| . . . | . . . | . 4a8 . |
| . . . | . . . | . .   . |
+-------+-------+---------+
| . . . | . . . | . .   . |
| . . . | . . . | . 36b . |
| . . . | . . . | . .   . |
+-------+-------+---------+
| . . . | . . . | . .   . |
| . . . | . . . | . .   . |
| . . . | . . . | . 469 . |
+-------+-------+---------+

The actual values shown are just for illustration. If I infer from the 4a, then r9c8 = 69. If I infer from the 6b, then r9c8 = 49. The 9 is there based on inferences from both a and b, so I placed it. Valid or did I just get lucky this one time?
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Asellus



Joined: 05 Jun 2007
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Location: Sonoma County, CA, USA

PostPosted: Tue Apr 01, 2008 8:37 pm    Post subject: Reply with quote

Marty wrote:
Valid or did I just get lucky this one time?

I believe that was luck. I don't see it as a valid placement. All you know is that r9c8 is either {69} or it is {49}. <4> and <6> are still possibilities.
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Marty R.



Joined: 12 Feb 2006
Posts: 5123
Location: Rochester, NY, USA

PostPosted: Tue Apr 01, 2008 9:22 pm    Post subject: Reply with quote

As always, thanks. I guess I'll avoid that type of thing in the future. But I do understand what you're saying.
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