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Logic Sept 24

 
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tm6001



Joined: 24 Sep 2005
Posts: 1
PostPosted: Sat Sep 24, 2005 3:58 pm    Post subject: Logic Sept 24 Reply with quote
Sept 24 puzzle today. I am here:
-6- --5 ---
5-- -7- 9--
743 169 8--

--4 -81 --7
-1- --- -8-
2-- -5- 1--

1-- 634 298
4-6 -9- --1
--- 51- -4-

The hint says 9 in row 6 column 9. I don't get the logic.
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chobans



Joined: 21 Aug 2005
Posts: 39
PostPosted: Sat Sep 24, 2005 5:36 pm    Post subject: Reply with quote
r3c8 and r3c9 can only be {2,5} so you can eliminate 2 and 5 from other cells in box 3(r1c7-r3c9). So you get {3,4} at r1c9 and {3,4,6} at r2c9.

r1c9 - {3,4}, r2c9 - {3,4,6}, r6c9 - {3,4,6,9}, r9c9 - {3,6}

Naked quadruple. So you can eliminate 3,4,6 and 9 from other cells in column 9. So r5c9 becomes {2,5}.

So after these elimination, 9 can ONLY go at r6c9 in box 6. It's easily solvable after this.
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Alnasi
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PostPosted: Sat Sep 24, 2005 7:51 pm    Post subject: A Naked what? Reply with quote
OK call me stupid. I had taken the first step in you solution, but I don't understand the "naked quadruple." How does that eliminate all but 2 and 5 from r5c9?
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
PostPosted: Sat Sep 24, 2005 8:15 pm    Post subject: Re: A Naked what? Reply with quote
Alnasi wrote:
OK call me stupid. I had taken the first step in you solution, but I don't understand the "naked quadruple." How does that eliminate all but 2 and 5 from r5c9?


I'll try to help explain Chobans' very concise description of the logic. At the point you have reached in the puzzle we have the following possibilities in column 9:

r1c9 = {3, 4}
r2c9 = {3, 4, 6}
r3c9 = {2, 5}
r4c9 = 7
r5c9 = ?
r6c9 = {3, 4, 6, 9}
r7c9 = 8
r8c9 = 1
r9c9 = {3, 6}

Examining this list and supposing we have no knowledge of the possible contents of r5c9 we see that the four cells r1c9, r2c9, r6c9, and r9c9 (the "naked quadruple[t]") must contain the four values 3, 4, 6, and 9 in some order. Since the values 1, 7, and 8 are already filled in, there are only two possibilities left for r5c9 -- {2, 5}.

Another way to reason about this is to observe that {3, 4, 6, 9} must fit in r1c9/r2c9/r6c9/r9c9 in some order -- that's four values in four boxes. And from the list above, the "9" has to go at r6c9, leaving {3, 4, 6} in r1c9/r2c9/r9c9. dcb
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datraega
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PostPosted: Sun Sep 25, 2005 3:06 pm    Post subject: Re: A Naked what? Reply with quote
David Bryant wrote:
Alnasi wrote:
OK call me stupid. I had taken the first step in you solution, but I don't understand the "naked quadruple." How does that eliminate all but 2 and 5 from r5c9?


I'll try to help explain Chobans' very concise description of the logic. At the point you have reached in the puzzle we have the following possibilities in column 9:

r1c9 = {3, 4}
r2c9 = {3, 4, 6}
r3c9 = {2, 5}
r4c9 = 7
r5c9 = ?
r6c9 = {3, 4, 6, 9}
r7c9 = 8
r8c9 = 1
r9c9 = {3, 6}

Examining this list and supposing we have no knowledge of the possible contents of r5c9 we see that the four cells r1c9, r2c9, r6c9, and r9c9 (the "naked quadruple[t]") must contain the four values 3, 4, 6, and 9 in some order. Since the values 1, 7, and 8 are already filled in, there are only two possibilities left for r5c9 -- {2, 5}.

Another way to reason about this is to observe that {3, 4, 6, 9} must fit in r1c9/r2c9/r6c9/r9c9 in some order -- that's four values in four boxes. And from the list above, the "9" has to go at r6c9, leaving {3, 4, 6} in r1c9/r2c9/r9c9. dcb


Ehm, I think FROM the fact that r3c8 and r3c9 can only be {2,5} FOLLOWS that {3, 4, 6, 9} must fit in r1c9/r2c9/r6c9/r9c9 in some order. Not vice versa.

Look at the (completed) list.

r1c9 = {3, 4}
r2c9 = {3, 4, 6}
r3c9 = {2, 5}
r4c9 = 7
r5c9 = {2, 3, 4, 5, 6, 9}
r6c9 = {3, 4, 6, 9}
r7c9 = 8
r8c9 = 1
r9c9 = {3, 6}

2 and 5 only fit in r3c9 and r5c9. Therefore, r5c9 reduces to {2, 5}.
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