The New Sudoku Players' Forum

[The Robman]

The Chicago Tribune has started running Sudoku puzzles in today's paper. (They don't appear to be pappocom puzzles).

Here's the introductory article...
http://www.chicagotribune.com/features/lifestyle/q/chi-0509040468sep04,1,2528323.story

I coldn't find the puzzle itself on their web site, so here's today's puzzle (rated "tough")...

Code: Select all

.|.|.|.|.|.|.|.|.
.|7|8|2|.|6|3|1|.
6|9|.|.|.|.|.|5|2
-----+-----+-----
.|.|7|9|.|1|4|.|.
.|6|.|.|.|.|.|7|.
.|.|3|6|.|8|5|.|.
-----+-----+-----
3|8|.|.|.|.|.|4|7
.|2|5|1|.|3|6|9|.
.|.|.|.|.|.|.|.|.

[DoubleB72]

I have been on this thing for a whole day and can't get it

[r.e.s.]

That's the same one as in Sunday's LA Times 2005-09-04. Let me try to neaten up the formatting:

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| . 7 8 | 2 . 6 | 3 1 . |
| 6 9 . | . . . | . 5 2 |
+-------+-------+-------+
| . . 7 | 9 . 1 | 4 . . |
| . 6 . | . . . | . 7 . |
| . . 3 | 6 . 8 | 5 . . |
+-------+-------+-------+
| 3 8 . | . . . | . 4 7 |
| . 2 5 | 1 . 3 | 6 9 . |
| . . . | . . . | . . . |
+-------+-------+-------+

I couldn't solve it with pencil & paper (without guessing). With some software assistance, however, I was able to solve it by finding seven forcing chains of lengths 4,5,8,8,8,8,8 (not in that order) and one forcing "net" (which the software could not find) involving 14 cells (whew!).

On the other hand, for those who like to solve by guessing ...
I was amazed to notice that, at the start, there is one particular cell with only two candidates such that guessing the correct candidate leads to a complete solution with nothing more than naked- & hidden-singles (kind of like bowling a strike with 81 pins ;o)!

[DoubleB72]

i guess i should mention i am somewhat new, but good at these. Either way, I really didn't understand your reply. But, thanks
DoubleB

[r.e.s.]

i guess i should mention i am somewhat new, but good at these. Either way, I really didn't understand your reply. But, thanks
DoubleB

There's a simple description of forcing chains at http://www.simes.clara.co.uk/programs/sudokutechnique7.htm
A good way to learn (both Pappocom & non-Pappocom) solving methods is to use some software that lets you single-step through the solving while it displays an explanation of what it's doing at each step. I find the free software at http://www.madoverlord.com/projects/sudoku.t to be excellent for this.

BTW ...
With a bit more searching, I was able to find a solution using five forcing chains (four of length 8 and one of length 12). I'm pretty sure that can be further improved.

[tso]

I had stopped even looking at the puzzles in the LA Times because they had become ridiculously easy -- puzzles that Pappocom would rate as no more than Medium rated as Diabolical. Maybe they heard our complaints, as this puzzle is actually difficult -- and so far, I don't know how to complete it without taking the easy way out. I'll have to start looking at the Times again.

[r.e.s.]

tso ...

Well, this one is certainly different. Their rating system still seems wacko (this puzzle being rated as merely "tough") .

I've reduced my solution to using four forcing chains, each of length 8; however, I'm unsure whether it's appropriate to post it in this forum (and if so, whether it should be here or in the section on solving techniques, even though it's non-Pappocom).

[tso]

This is exactly the right place to post anything about a non-pappocom puzzle.

So far, I have not been able to find a clever solution -- certainly nothing worth posting.

[r.e.s.]

This is exactly the right place to post anything about a non-pappocom puzzle.

So far, I have not been able to find a clever solution -- certainly nothing worth posting.

Thanks for the reply. I'll have to let others judge whether this is worth it ...

Puzzle from the L.A. Times 2005-09-04:

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| . 7 8 | 2 . 6 | 3 1 . |
| 6 9 . | . . . | . 5 2 |
+-------+-------+-------+
| . . 7 | 9 . 1 | 4 . . |
| . 6 . | . . . | . 7 . |
| . . 3 | 6 . 8 | 5 . . |
+-------+-------+-------+
| 3 8 . | . . . | . 4 7 |
| . 2 5 | 1 . 3 | 6 9 . |
| . . . | . . . | . . . |
+-------+-------+-------+

EDIT: The method uses four forcing nets (three of which are chains), each involving 8 cells.

Here's a sketch, omitting only naked- & hidden-single exclusions:

---Preliminaries---
Preliminary simple exclusions (using the naked pair 12-12 in c7,
and the 4's locked in r5 box 5) lead to the candidate grid

Code: Select all

{1245} {3}    {124}  {478}  {1589} {4579} {789}  {68}   {469} 
{45}   {7}    {8}    {2}    {59}   {6}    {3}    {1}    {49}   
{6}    {9}    {14}   {3478} {138}  {47}   {78}   {5}    {2}   
{28}   {5}    {7}    {9}    {23}   {1}    {4}    {68}   {36}   
{1289} {6}    {129}  {34}   {235}  {245}  {89}   {7}    {139} 
{149}  {14}   {3}    {6}    {7}    {8}    {5}    {2}    {19}   
{3}    {8}    {169}  {5}    {269}  {29}   {12}   {4}    {7}   
{7}    {2}    {5}    {1}    {4}    {3}    {6}    {9}    {8}   
{149}  {14}   {1469} {78}   {2689} {279}  {12}   {3}    {5}   

---Forcing net #1---
EDIT: This is a "net" but not a chain, in the sense that what's to the right of a '=>' is not always implied by the immediately preceding step alone. (What's to the right of a '=>' is implied by the steps that collectively precede it.)
r2c1 = {4}
=> r3c3 = {1}
=> r1c3 = {2}
=> r5c3 = {9}
=> r5c7 = {8}
=> r3c7 = {7}
=> r1c7 = {9}
=> r2c9 = {4}
=> r2c1 = {5} (contradiction);
therefore r2c1 =/= {4}, which leads to

Code: Select all

{124}  {3}    {124}  {478}  {158}  {457}  {789}  {68}   {69}   
{5}    {7}    {8}    {2}    {9}    {6}    {3}    {1}    {4}   
{6}    {9}    {14}   {3478} {138}  {47}   {78}   {5}    {2}   
{28}   {5}    {7}    {9}    {23}   {1}    {4}    {68}   {36}   
{1289} {6}    {129}  {34}   {235}  {245}  {89}   {7}    {139} 
{149}  {14}   {3}    {6}    {7}    {8}    {5}    {2}    {19}   
{3}    {8}    {169}  {5}    {26}   {29}   {12}   {4}    {7}   
{7}    {2}    {5}    {1}    {4}    {3}    {6}    {9}    {8}   
{149}  {14}   {1469} {78}   {268}  {279}  {12}   {3}    {5}   

---Forcing net #2 (a chain)---
r1c4 = {4}
=> r5c4 = {3}
=> r4c5 = {2}
=> r4c1 = {8}
=> r4c8 = {6}
=> r1c8 = {8}
=> r3c7 = {7}
=> r3c6 = {4}
=> r1c4 = {7,8} (contradiction);
therefore r1c4 =/= {4}, and simple exclusions (using the
hidden pair 34-34 in c4, and naked quad 6789 in r1) lead to

Code: Select all

{124}  {3}    {124}  {78}   {15}   {45}   {789}  {68}   {69}   
{5}    {7}    {8}    {2}    {9}    {6}    {3}    {1}    {4}   
{6}    {9}    {14}   {34}   {138}  {47}   {78}   {5}    {2}   
{28}   {5}    {7}    {9}    {23}   {1}    {4}    {68}   {36}   
{1289} {6}    {129}  {34}   {235}  {245}  {89}   {7}    {139} 
{149}  {14}   {3}    {6}    {7}    {8}    {5}    {2}    {19}   
{3}    {8}    {169}  {5}    {26}   {29}   {12}   {4}    {7}   
{7}    {2}    {5}    {1}    {4}    {3}    {6}    {9}    {8}   
{149}  {14}   {1469} {78}   {268}  {279}  {12}   {3}    {5}   

---Forcing net #3 (a chain)---
r3c4 = {4}
=> r3c6 = {7}
=> r3c7 = {8}
=> r1c8 = {6}
=> r4c8 = {8}
=> r4c1 = {2}
=> r4c5 = {3}
=> r5c4 = {4}
=> r3c4 = {3} (contradiction);
therefore r3c4 =/= {4}, which leads to

Code: Select all

{124}  {3}    {124}  {78}   {15}   {45}   {789}  {68}   {69}   
{5}    {7}    {8}    {2}    {9}    {6}    {3}    {1}    {4}   
{6}    {9}    {14}   {3}    {18}   {47}   {78}   {5}    {2}   
{28}   {5}    {7}    {9}    {23}   {1}    {4}    {68}   {36}   
{1289} {6}    {129}  {4}    {235}  {25}   {89}   {7}    {139} 
{149}  {14}   {3}    {6}    {7}    {8}    {5}    {2}    {19}   
{3}    {8}    {169}  {5}    {26}   {29}   {12}   {4}    {7}   
{7}    {2}    {5}    {1}    {4}    {3}    {6}    {9}    {8}   
{149}  {14}   {1469} {78}   {268}  {279}  {12}   {3}    {5}   

---Forcing net #4 (a chain)---
r1c8 = {8}
=> r1c4 = {7}
=> r3c6 = {4}
=> r1c6 = {5}
=> r5c6 = {2}
=> r4c5 = {3}
=> r4c9 = {6}
=> r4c8 = {8}
=> r1c8 = {6} (contradiction);
therefore r1c8 =/= {8}, which leads to the solution

Code: Select all

+-------+-------+-------+
| 1 3 2 | 8 5 4 | 7 6 9 |
| 5 7 8 | 2 9 6 | 3 1 4 |
| 6 9 4 | 3 1 7 | 8 5 2 |
+-------+-------+-------+
| 2 5 7 | 9 3 1 | 4 8 6 |
| 8 6 1 | 4 2 5 | 9 7 3 |
| 9 4 3 | 6 7 8 | 5 2 1 |
+-------+-------+-------+
| 3 8 9 | 5 6 2 | 1 4 7 |
| 7 2 5 | 1 4 3 | 6 9 8 |
| 4 1 6 | 7 8 9 | 2 3 5 |
+-------+-------+-------+

(*If* guessing were allowed, the single guess r1c8 = 6 at the very start would lead to the solution using only naked- & hidden-singles!)

[r.e.s.]

Alternatively, this forcing net* involving 18 cells is enough:
r1c8 = {8}
=> r3c7 = {7}
=> r3c6 = {4}
=> r3c3 = {1}
=> r6c8 = {2}
=> r7c4 = {5}
=> r8c9 = {8}
=> r9c8 = {3}
=> r4c4 = {6}
=> r4c9 = {3}
=> r4c2 = {5}
=> r4c5 = {2}
=> r5c6 = {5}
=> r1c7 = {9}
=> r1c6 = {7}
=> r1c4 = {3}
=> r3c4 = {8}
=> r3c5 = {} (contradiction);
therefore, r1c8 =/= {8}, and simple exclusions (only naked- & hidden-singles) then lead to the solution.

*EDIT: Changed the name to "net" rather than "chain", as explained in the previous post.

[DoubleB72]

what exactly are naked pairs? Also, I had the exact same candidates you did except in r5c1 I thought you could use a 4. And then in r6c9, I thought 3 could be possibly used. What eliminated them? Finally, how do you know where to start a forcing chain? Can you use any box that only has 2 candidated in it or only certain ones will work?

thanks for all your help

B

[DoubleB72]

Please ignore my comments on the 4 in r5c1 and the 3 in r6c9... I am a moron on that one
sorry

[r.e.s.]

Sorry for the delay ...

what exactly are naked pairs?

There's a nice description at http://www.simes.clara.co.uk/programs/sudokutechnique5.htm
(also see the other techniques described there, including forcing chains).

Finally, how do you know where to start a forcing chain? Can you use any box that only has 2 candidated in it or only certain ones will work?

Forcing chains exist only for certain candidates in certain starting cells. People have tried to describe their techniques for finding a variety of different types of forcing chain, but it's typically a very tedious process (both to perform and to describe). Searching this forum's section on Solving Techniques might turn up something useful.

[tso]

Sorry for the delay ...

what exactly are naked pairs?

There's a nice description at http://www.simes.clara.co.uk/programs/sudokutechnique5.htm
(also see the other techniques described there, including forcing chains).

Finally, how do you know where to start a forcing chain? Can you use any box that only has 2 candidated in it or only certain ones will work?

Forcing chains exist only for certain candidates in certain starting cells. People have tried to describe their techniques for finding a variety of different types of forcing chain, but it's typically a very tedious process (both to perform and to describe). Searching this forum's section on Solving Techniques might turn up something useful.

While I can't argue that describing techniques for finding forcing chains isn't tedious, the methods themselves often are not. I can find -- or reach the point where I know I will not find -- forcing chains (at least of the xy-chain type) much more quickly then I can find a swordfish even if I know one is there. For that matter, finding a string of hidden and/or naked singles is by far the most tedious part of solving, much more susceptible to errors and oversights.

[r.e.s.]

While I can't argue that describing techniques for finding forcing chains isn't tedious, the methods themselves often are not. I can find -- or reach the point where I know I will not find -- forcing chains (at least of the xy-chain type) much more quickly then I can find a swordfish even if I know one is there.

I believe you! But I also believe that most people -- e.g. Wayne's huge target audience -- would find searching for swordfish to also fall in the "overly tedious" category (I suppose "overly demanding" would be more accurate).