View previous topic :: View next topic 
Author 
Message 
tm6001
Joined: 24 Sep 2005 Posts: 1

Posted: Sat Sep 24, 2005 3:58 pm Post subject: Logic Sept 24 


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
46 9 1
 51 4
The hint says 9 in row 6 column 9. I don't get the logic. 

Back to top 


chobans
Joined: 21 Aug 2005 Posts: 39

Posted: Sat Sep 24, 2005 5:36 pm Post subject: 


r3c8 and r3c9 can only be {2,5} so you can eliminate 2 and 5 from other cells in box 3(r1c7r3c9). 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. 

Back to top 


Alnasi Guest

Posted: Sat Sep 24, 2005 7:51 pm Post subject: A Naked what? 


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? 

Back to top 


David Bryant
Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Posted: Sat Sep 24, 2005 8:15 pm Post subject: Re: A Naked what? 


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 

Back to top 


datraega Guest

Posted: Sun Sep 25, 2005 3:06 pm Post subject: Re: A Naked what? 


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}. 

Back to top 




You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot vote in polls in this forum

Powered by phpBB © 2001, 2005 phpBB Group
