What can I work out from here... ?

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What can I work out from here... ?

Postby rik » Wed Jun 14, 2006 4:36 pm

Hi all,

I've got a puzzle here where one of the blocks looks like this:

Code: Select all
  5            4    {7, 8}
  {3, 6, 8}    2    {6, 8}
  {3, 7, 8}    1    9


Where {x, y .. } indicates that the cell must contain one of x, y, ...

(I didn't see a standard notation, so I've come up with this in the hope that it's not too confusing).

Let us refer to:
the {7, 8} choice as A
the {3, 6, 8} choice as B
the {6, 8} choice as C
the {3, 7, 8} choice as D

Now, given an analysis of (what I understand of) naked pairs, we get:
- A and D are 7 and 8
- B and C are 6 and 8
- one of B and D MUST be 3.

If the first statement holds true, then the 3 choice can be removed from B. This means that B must hold 3, which means that C holds 6, which leaves A and D. However, the same logic holds for the second statement, with A swapped for C and B swapped for D.

The question I have is - have I missed anything about this situation? Is there anything else I can work out with the information given? It feels like I should...
rik
 
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Joined: 14 June 2006

while we're at it...

Postby rik » Wed Jun 14, 2006 4:50 pm

I have a boxrow that reads:

Code: Select all
{1, 2}  {1, 3}  {1, 2, 3}


Where {1, 2} indicates that only 1 and 2 are the valid choices for this cell.

Can I use the hidden/naked pairs rules on this to say that the boxrow should be 2, 1 3, in this case?
rik
 
Posts: 3
Joined: 14 June 2006

Re: while we're at it...

Postby ronk » Wed Jun 14, 2006 5:14 pm

rik wrote:I have a boxrow that reads:

Code: Select all
{1, 2}  {1, 3}  {1, 2, 3}

(...)
Can I use the hidden/naked pairs rules on this to say that the boxrow should be 2, 1 3, in this case?

As it stands, that is a naked triple, i.e, 3 candidates for 3 cells. If it were reducible, there would be either a naked single (with a complementary hidden pair) ... or a hidden single (with a complementary naked pair). If either a naked or hidden single existed ...

digit 1 would exist in only one cell, or
digit 2 would exist in only one cell, or
digit 3 would exist in only one cell.

Since neither is true, your naked triple is irreducible. By a similar though more complex argument, it can be shown that your first example is not reducible either.
ronk
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Postby rik » Wed Jun 14, 2006 5:42 pm

ahh. i understand.

thank you.
rik
 
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Joined: 14 June 2006

Postby keith » Wed Jun 14, 2006 9:58 pm

rik,

Suppose your first example was:
Code: Select all
5            4    {7, 8}
{3, 6, 8}    2    {7, 8}
{3, 7, 8}    1    9

Then, {7, 8} are indeed a naked pair. You can reduce this to
Code: Select all
5         4    {7, 8}
{3, 6}    2    {7, 8}
{3}       1    9

etc.

Keith
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