The New Sudoku Players' Forum

by **FRANKH** » Fri Jan 27, 2006 11:41 pm

Can someone explain the third move ...after the 2 and 5 in the top middle box

by **CathyW** » Sat Jan 28, 2006 12:03 am

If you could post the puzzle for those of us who don't get USA Today we might be able to help!

by **FRANKH** » Sat Jan 28, 2006 12:13 am

I'm new to this forum, so bear with me. How do I write down the puzzle so the columns line up?[/code]

by **FRANKH** » Sat Jan 28, 2006 12:22 am

*****12**
*3**245**
*62*57***
5***6***7
2***4***8
9***3***1
***4**19*
**85***6*
**42*****

by **CathyW** » Sat Jan 28, 2006 12:58 am

Check the sticky post at the top of this forum for guidance on posting puzzles that you want help with. You can get numbers to line up by using a fixed pitch font like courier when typing them up in Word or similar, and then copy and paste within code (or I use Simple Sudoku which allows you to copy a puzzle and paste the original puzzle and candidate list as below!).

Code: Select all: *-----------* |...|..1|2..| |.3.|.24|5..| |.62|.57|...| |---+---+---| |5..|.6.|..7| |2..|.4.|..8| |9..|.3.|..1| |---+---+---| |...|4..|19.| |..8|5..|.6.| |..4|2..|...| *-----------* {478} {45789} {579} {3689} {89} {1} {2} {3478} {3469} {178} {3} {179} {689} {2} {4} {5} {178} {69} {148} {6} {2} {389} {5} {7} {3489} {1348} {349} {5} {148} {13} {189} {6} {289} {349} {234} {7} {2} {17} {1367} {179} {4} {59} {369} {35} {8} {9} {478} {67} {78} {3} {258} {46} {245} {1} {367} {257} {3567} {4} {78} {368} {1} {9} {235} {137} {1279} {8} {5} {179} {39} {347} {6} {234} {1367} {1579} {4} {2} {1789} {3689} {378} {3578} {35}

My next move would be to examine box 4 for a hidden pair, but there's plenty of other eliminations that can be done from locked candidates and a couple of x-wings.

Let us know if you need any more.

by **FRANKH** » Sat Jan 28, 2006 1:10 am

I saw the locked pair in box 4 and also row 6, but I still couldn't figure out the next move

by **Cec** » Sat Jan 28, 2006 3:15 am

FRANKH wrote:I saw the locked pair in box 4 and also row 6, but I still couldn't figure out the next move

Hi Frank,
I may be wrong but I'm not sure you fully understand about "hidden pairs" and "Locked Candidates". You could read about these and other techniques by clicking on HERE and HERE.

In the meantime to get you further along, look at box 4 and column 2 (c2) and try spotting the "hidden pair" being two numbers which only appear in two cells but nowhere else within this box 4. These candidates can therefore be excluded if existing in other cells in c2 outside box 4.

Also in box 4, notice the 6's are "locked" or restricted solely to c3. This means any other 6's can be excluded from c3 outside box 4. There are other "Locked Candidate" situations such as in c8 and c7. As Cathy mentions above, a knowledge of "X-wings" is necessary to complete this puzzle.

Cec

by **FRANKH** » Sat Jan 28, 2006 4:49 am

I must be having an off day or maybe I'm just stupid, but I still don't see the next move. I see the hidden pairs (48 in box 4 and 25 in row 6) and I see several locked candidates, but I don't see an obvious next move. What is it?

by **Cec** » Sat Jan 28, 2006 6:12 am

FRANKH wrote:"..I see several locked candidates, but I don't see an obvious next move. What is it?"

After standard "Locked Candidate" eliminations, I suspect I've reached the same stalemate. My pencilmark grid is this:

Code: Select all: *-----------------------------------------------------------* | 478 57 579 | 3689 89 1 | 2 3478 3469 | | 178 3 179 | 689 2 4 | 5 178 69 | | 148 6 2 | 389 5 7 | 348 1348 349 | |-------------------+-------------------+-------------------| | 5 48 13 | 189 6 289 | 349 234 7 | | 2 17 1367 | 179 4 59 | 369 35 8 | | 9 48 67 | 78 3 25 | 46 245 1 | |-------------------+-------------------+-------------------| | 367 257 57 | 4 78 368 | 1 9 235 | | 137 1279 8 | 5 179 39 | 347 6 234 | | 1367 1579 4 | 2 179 369 | 378 38 35 | *-----------------------------------------------------------*

Identifying X-wings continues to baffle me but here goes: For the candidate 9's in rows 8 and 9 does r8c26 and r9c26 identify an X-wing which would then exclude the remaining 9's from r8c5 and r9c5? Help would be welcome.

Cec

by **tso** » Sat Jan 28, 2006 6:36 am

cecbevwr wrote:
FRANKH wrote:"..I see several locked candidates, but I don't see an obvious next move. What is it?"

After standard "Locked Candidate" eliminations, I suspect I've reached the same stalemate. My pencilmark grid is this:
Code: Select all
*-----------------------------------------------------------* | 478 57 579 | 3689 89 1 | 2 3478 3469 | | 178 3 179 | 689 2 4 | 5 178 69 | | 148 6 2 | 389 5 7 | 348 1348 349 | |-------------------+-------------------+-------------------| | 5 48 13 | 189 6 289 | 349 234 7 | | 2 17 1367 | 179 4 59 | 369 35 8 | | 9 48 67 | 78 3 25 | 46 245 1 | |-------------------+-------------------+-------------------| | 367 257 57 | 4 78 368 | 1 9 235 | | 137 1279 8 | 5 179 39 | 347 6 234 | | 1367 1579 4 | 2 179 369 | 378 38 35 | *-----------------------------------------------------------*

Identifying X-wings continues to baffle me but here goes: For the candidate 9's in rows 8 and 9 does r8c26 and r9c26 identify an X-wing which would then exclude the remaining 9's from r8c5 and r9c5? Help would be welcome.

Cec

This is not an X-wing.

Here are the 9's at this point:

Code: Select all: *-----------------------* | . . 9 | 9 9 . | . . 9 | | . . 9 | 9 . . | . . 9 | | . . . | 9 . . | . . 9 | *-----------------------* | . . . | 9 . 9 | 9 . . | | . . . | 9 . 9 | 9 . . | | 9 . . | . . . | . . . | *-----------------------* | . . . | . . . | . 9 . | | . 9 . | . 9 9 | . . . | | . 9 . | . 9 9 | . . . | *-----------------------*

There is no x-wing in 9s. In fact, I don't believe there are *any* simple or intermediate tactics left -- no unique rectangles, no pairs, no triples, no quads, no xy-wings, no simple forcing chains, no coloring. The next step will require some creativity. Surprising that USA Today would have a puzzle this hard -- of course they did rate it five stars.

I don't have a solution yet.

by **Cec** » Sat Jan 28, 2006 9:14 am

Thanks tso for your prompt reply. More homework for me to again read up on X-wing identification.
My experience with this thread supports Animator's efforts to encourage puzzles to be submitted as suggested in the "Sticky New topics - How to ask for help" at the start of the Forum.
Posting the initial puzzle, the candidate grid showing how far the person progressed (and hence what they know) and the difficulty level would clearly help in replying. Apart from getting over my depth in trying to help, it would now appear my above suggestions would have been known.

Cec

by **tarek** » Sat Jan 28, 2006 10:50 am

A suggested next move would be (using a double multi-implication chain):

Code: Select all: *--------------------------------------------------------* | 478 57 579 | 3689 89 1 | 2 3478 3469 | | 178 3 179 | 689 2 4 | 5 178 69 | | 148 6 2 | 389 5 7 | 348 1348 349 | |------------------+------------------+------------------| | 5 48 13 | 189 6 289 | 349 234 7 | | 2 17 1367 | 179 4 59 | 369 35 8 | | 9 48 67 | 78 3 25 | 46 25 1 | |------------------+------------------+------------------| | 367 257 57 | 4 78 368 | 1 9 235 | | 137 1279 8 | 5 179 39 | 347 6 234 | | 1367 1579 4 | 2 179 369 | 378 38 35 | *--------------------------------------------------------* Candidates in r7c3 will force r1c2 to have only 5 as valid Candidates r7c3=5 => r1c3<>5 => r1c2=5 r7c3=7 => (r5c3 <>7 r6c3=6) => r6c7=4 => r6c2=8 => r6c4=7 => r5c4<>7 => r5c2=7 => r1c2=5 Therefore r1c2=5

This however doesn't solve the puzzle & several other (but simpler) chains are still needed acccording to my solver. I'm sure there are other simpler ways, as my solver has yet to implement colouring, Uniqueness, BUG,.... There are bound to be simpler methods.

These are the steps to solve the puzzle:

Code: Select all: *--------------------------------------------------------* | 478 5 79 | 3689 89 1 | 2 3478 3469 | | 178 3 179 | 689 2 4 | 5 178 69 | | 148 6 2 | 389 5 7 | 348 1348 349 | |------------------+------------------+------------------| | 5 48 13 | 189 6 289 | 349 234 7 | | 2 17 1367 | 179 4 59 | 369 35 8 | | 9 48 67 | 78 3 25 | 46 25 1 | |------------------+------------------+------------------| | 367 27 5 | 4 78 368 | 1 9 23 | | 137 1279 8 | 5 179 39 | 347 6 234 | | 1367 179 4 | 2 179 369 | 378 38 5 | *--------------------------------------------------------* Candidates in r4c8 will force r9c8 to have only 8 as valid Candidates r4c8=2: r4c8=2 => r6c8=5 => r5c8=3 => r9c8=8 r4c8=3: r4c8=3 => r9c8=8 r4c8=4: r4c8=4 => r6c7=6 => r6c3=7 => r1c3=9 => r1c5=8 => r7c5=7 => r7c2=2 => r7c9=3 => r9c8=8 Threfore r9c8=8 *--------------------------------------------------------* | 478 5 79 | 3689 89 1 | 2 347 3469 | | 178 3 179 | 689 2 4 | 5 17 69 | | 14 6 2 | 39 5 7 | 8 134 349 | |------------------+------------------+------------------| | 5 48 13 | 189 6 289 | 349 234 7 | | 2 17 1367 | 179 4 59 | 369 35 8 | | 9 48 67 | 78 3 25 | 46 25 1 | |------------------+------------------+------------------| | 367 27 5 | 4 78 368 | 1 9 23 | | 137 1279 8 | 5 179 39 | 347 6 234 | | 1367 179 4 | 2 179 369 | 37 8 5 | *--------------------------------------------------------* Eliminating 7 From r9c2 (2 & 3 in r7c9 form an XY wing with 7 in r7c2 & r9c7) Eliminating 7 From r9c1 (2 & 3 in r7c9 form an XY wing with 7 in r7c2 & r9c7) *--------------------------------------------------------* | 478 5 79 | 3689 89 1 | 2 347 3469 | | 178 3 179 | 689 2 4 | 5 17 69 | | 14 6 2 | 39 5 7 | 8 134 349 | |------------------+------------------+------------------| | 5 48 13 | 189 6 289 | 349 234 7 | | 2 17 1367 | 179 4 59 | 369 35 8 | | 9 48 67 | 78 3 25 | 46 25 1 | |------------------+------------------+------------------| | 367 27 5 | 4 78 368 | 1 9 23 | | 137 1279 8 | 5 179 39 | 347 6 234 | | 136 19 4 | 2 179 369 | 37 8 5 | *--------------------------------------------------------* Eliminating 7 From r2c1 (1 & 9 & 7 in r2c3 form an XYZ wing with r2c8 & r1c3) *--------------------------------------------------------* | 478 5 79 | 3689 89 1 | 2 347 3469 | | 18 3 179 | 689 2 4 | 5 17 69 | | 14 6 2 | 39 5 7 | 8 134 349 | |------------------+------------------+------------------| | 5 48 13 | 189 6 289 | 349 234 7 | | 2 17 1367 | 179 4 59 | 369 35 8 | | 9 48 67 | 78 3 25 | 46 25 1 | |------------------+------------------+------------------| | 367 27 5 | 4 78 368 | 1 9 23 | | 137 1279 8 | 5 179 39 | 347 6 234 | | 136 19 4 | 2 179 369 | 37 8 5 | *--------------------------------------------------------* Candidates in r8c7 will force r4c3 to have only 3 as valid Candidates r8c7=3: r8c7=3 => r7c9=2 => r7c2=7 => r5c2=1 => r4c3=3 r8c7=4: r8c7=4 => r6c7=6 => r6c3=7 => r5c2=1 => r4c3=3 r8c7=7: r8c7=7 => r9c7=3 => r7c9=2 => r7c2=7 => r5c2=1 => r4c3=3 *--------------------------------------------------------* | 478 5 79 | 3689 89 1 | 2 347 3469 | | 18 3 179 | 689 2 4 | 5 17 69 | | 14 6 2 | 39 5 7 | 8 134 349 | |------------------+------------------+------------------| | 5 48 3 | 1 6 289 | 49 24 7 | | 2 17 167 | 79 4 59 | 369 35 8 | | 9 48 67 | 78 3 25 | 46 25 1 | |------------------+------------------+------------------| | 367 27 5 | 4 78 368 | 1 9 23 | | 137 1279 8 | 5 179 39 | 347 6 234 | | 136 19 4 | 2 179 369 | 37 8 5 | *--------------------------------------------------------* Candidates in r8c7 will force r9c2 to have only 9 as valid Candidates r8c7=3: r8c7=3 => r7c9=2 => r7c2=7 => r5c2=1 => r9c2=9 r8c7=4: r8c7=4 => r6c7=6 => r6c3=7 => r5c2=1 => r9c2=9 r8c7=7: r8c7=7 => r9c7=3 => r7c9=2 => r7c2=7 => r5c2=1 => r9c2=9 Threfore r9c2=9 *--------------------------------------------------------* | 478 5 79 | 3689 89 1 | 2 347 3469 | | 18 3 179 | 689 2 4 | 5 17 69 | | 14 6 2 | 39 5 7 | 8 134 349 | |------------------+------------------+------------------| | 5 48 3 | 1 6 289 | 49 24 7 | | 2 17 167 | 79 4 59 | 369 35 8 | | 9 48 67 | 78 3 25 | 46 25 1 | |------------------+------------------+------------------| | 367 27 5 | 4 78 368 | 1 9 23 | | 137 127 8 | 5 179 39 | 347 6 234 | | 136 9 4 | 2 17 36 | 37 8 5 | *--------------------------------------------------------* Candidates in r5c3 will force r7c9 to have only 3 as valid Candidates r5c3=1: r5c3=1 => r5c2=7 => r7c2=2 => r7c9=3 r5c3=6: r5c3=6 => r6c3=7 => r1c3=9 => r1c5=8 => r7c5=7 => r7c2=2 => r7c9=3 r5c3=7: r5c3=7 => r1c3=9 => r1c5=8 => r7c5=7 => r7c2=2 => r7c9=3

If newspaper material was always like this :!:

Tarek

by **Carcul** » Sat Jan 28, 2006 12:17 pm

Tarek wrote:I'm sure there are other simpler ways, as my solver has yet to implement colouring, Uniqueness, BUG,....

Yes, there are other simpler ways. Here is one of them:

[r7c2]=2|9=[r1c3]-9-[r1c5]-8-[r7c5](-7-[r7c2])-7-[r7c3]-5-[r7c2]

(where I have used the AUR in cells r1c23/r7c23) which implies r7c2=2 and that solve the puzzle.

BTW Tarek, I am still waiting for your best shot.

Regards, Carcul

by **tarek** » Sat Jan 28, 2006 5:51 pm

Carcul wrote:BTW Tarek, I am still waiting for your best shot.

What a nice solution, I havent had time to do the full works on my generator. As the solver doesn't implement tests that depend on the single solution state, I can't gauge the difficulty fully. I could almost tell that it is difficult when the solver starts to use Nishio & guesses (eq to complex forcing chains), I haven't generated those yet, The best until now is this (intermediate difficulty, according to my solver slightly easier than #6 of the NICE loops exercises):

Code: Select all: Puzzle #4917 . . . | 3 . . | 8 . . . . . | . 4 6 | . . . . 1 . | 2 . . | . . 9 -------+-------+------ . 8 6 | . . . | . 7 . . 9 . | . . . | 2 1 . . . . | . . 2 | 6 . 3 -------+-------+------ 8 . . | . . . | 1 2 . . . 2 | 7 5 . | 3 . . . . 7 | . . 1 | . 5 .

More to come as I implement Uniqueness,AUR & BUG

Tarek

by **tso** » Sat Jan 28, 2006 7:19 pm

Carcul wrote:
Tarek wrote:I'm sure there are other simpler ways, as my solver has yet to implement colouring, Uniqueness, BUG,....

Yes, there are other simpler ways. Here is one of them:

[r7c2]=2|9=[r1c3]-9-[r1c5]-8-[r7c5](-7-[r7c2])-7-[r7c3]-5-[r7c2]

(where I have used the AUR in cells r1c23/r7c23) which implies r7c2=2 and that solve the puzzle.

As FRANKH is new to this forum, I'll try to paraphrase Carcul's solution in simple terms.

[r7c2]=2|9=[r1c3]-9-[r1c5]-8-[r7c5](-7-[r7c2])-7-[r7c3]-5-[r7c2]

Either r7c2=2 OR r1c3=9 OR both. This is because if this WEREN'T true, the four cells r17c23 could either be 5757 or 7575 and the puzzle would have two solutions.

[r7c2]=2|9=[r1c3]-9-[r1c5]-8-[r7c5](-7-[r7c2])-7-[r7c3]-5-[r7c2]

If r1c3=9, then r1c5=8, then r7c5=7

[r7c2]=2|9=[r1c3]-9-[r1c5]-8-[r7c5](-7-[r7c2])-7-[r7c3]-5-[r7c2]

If r7c5=7, then (r7c2<>7 AND r7c3=5), then r7c2=2

Putting it all together:

If r7c2<>2, then r1c3=9, then r1c5=8, then r7c5=7, then (r7c2<>7 AND r7c3=5), then r7c2=2 -- this is a contradiction, so r7c2 must be 2.

Here are the relevant cells:

Code: Select all: *-----------------------------------------------------------* | . 57 579 | . 89 . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | |-------------------+-------------------+-------------------| | . 257 57 | . 78 . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | *-----------------------------------------------------------*

Carcul --

a) Is that right?
b) How did you find this?
c) Should the reader be able to look at the nice loop notation you've given without seeing the grid and see that r7c2=2?

What I mean is, for example, in this simple situation ...

Code: Select all: *-------------------+-------------------+-------------------* | . . . | . . . | . . . | | . . . | . . . | . . . | | . . 12 | 23 . . | . . . | |-------------------+-------------------+-------------------| | . . 13 | 34 . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | |-------------------+-------------------+-------------------|

... this nice loop applies:
[r4c4]-3-[r4c3]-1-[r3c3]-2-[r3c4]-3-[r4c4]

Without seeing the grid, I can look at the nice loop notation and see that r4c4<>3.

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