The New Sudoku Players' Forum

by **eleven** » Thu Apr 03, 2008 7:46 am

Code: Select all: +-----------------------------------------------------------------------------------------+ | 1468 9 1347 | 1578 1457 4578 | 13578 14568 2 | | 5 2467 147 | 3 1247 24789 | 1789 14689 146789 | | 1248 2347 1347 | 6 12457 245789 | 135789 14589 1345789 | |-----------------------------+-----------------------------+-----------------------------| | 3 125 6 | 2579 257 257 | 4 12589 15789 | | 249 245 459 | 2457 8 1 | 2357 256 3567 | | 7 1245 8 | 2459 36 36 | 1259 1259 159 | |-----------------------------+-----------------------------+-----------------------------| | 146 8 13457 | 157 9 34567 | 125 1245 145 | | 1469 4567 2 | 1578 14567 45678 | 1589 3 14589 | | 149 345 13459 | 1258 12345 23458 | 6 7 14589 | +-----------------------------------------------------------------------------------------+

Either r7c1=6 or r7c6=6 -> r7c3=3 -> r8c2=7 -> r2c2=6, i.e. r1c1<>6, r8c2<>6 [corrected typo]

by **hobiwan** » Thu Apr 03, 2008 9:30 am

daj95376 wrote:This 17 isn't difficult if you find an elimination on candidate 4. What does it take without eliminating candidate 4???

Code: Select all
.1.7.........5.4..........34..3.....2.....5.....1...8.5...2.6...3.....7......4... #15709 # note: Simple Sudoku takes forever to verify a single solution # note: after SSTS, finned Swordfish present but not useful +-----------------------------------------------------------------------------------------+ | 3689 1 2345689 | 7 34689 3689 | 289 2569 25689 | | 36789 26789 236789 | 2689 5 13689 | 4 1269 126789 | | 6789 2456789 256789 | 24689 1689 1689 | 12789 12569 3 | |-----------------------------+-----------------------------+-----------------------------| | 4 56789 156789 | 3 6789 25 | 1279 1269 12679 | | 2 6789 136789 | 4689 6789 6789 | 5 13469 1679 | | 3679 5679 35679 | 1 4679 25 | 2379 8 24679 | |-----------------------------+-----------------------------+-----------------------------| | 5 4789 789 | 89 2 37 | 6 1349 189 | | 689 3 24689 | 5689 1689 1689 | 289 7 24589 | | 1 26789 26789 | 5689 37 4 | 2389 2359 2589 | +-----------------------------------------------------------------------------------------+

Discontinuous Nice Loop [r1c3]=4=[r1c5]=3=[r9c5]-3-[r7c6]=3=[r7c8]=4=[r7c2]-4-[r3c2]=4=[r1c3] => [r1c3]<>235689 (or [r1c3]=4)
Does setting 4 instead of eliminating 4 qualify?

by **hobiwan** » Thu Apr 03, 2008 9:36 am

daj95376 wrote:I settled on an implication chain that results in a contradiction. Maybe you'll have better luck.

Code: Select all
.9......25..3........6.....3.6...4......81...7.........8..9......2....3.......67. #24299 +-----------------------------------------------------------------------------------------+ | 1468 9 1347 | 1578 1457 4578 | 13578 14568 2 | | 5 2467 147 | 3 1247 24789 | 1789 14689 146789 | | 1248 2347 1347 | 6 12457 245789 | 135789 14589 1345789 | |-----------------------------+-----------------------------+-----------------------------| | 3 125 6 | 2579 257 257 | 4 12589 15789 | | 249 245 459 | 2457 8 1 | 2357 256 3567 | | 7 1245 8 | 2459 36 36 | 1259 1259 159 | |-----------------------------+-----------------------------+-----------------------------| | 146 8 13457 | 157 9 34567 | 125 1245 145 | | 1469 4567 2 | 1578 14567 45678 | 1589 3 14589 | | 149 345 13459 | 1258 12345 23458 | 6 7 14589 | +-----------------------------------------------------------------------------------------+

Code: Select all
[r6c6]=3 [r7c3]=3 [r3c2]=3 [r5c9]=3 [r5c8]=6 [r1c1]=6 => [r8c2b7]=67 contradiction!

Discontinuous Nice Loop (again): [r2c2]=6=[r8c2]=7=[r7c3]=3=[r7c6]=6=[r7c1]-6-[r1c1]=6=[r2c2] => [r2c2]<>247 (or [r2c2]=6)

by **eleven** » Thu Apr 03, 2008 10:33 am

The "short version" would be enough:
6=[r8c2]=7=[r7c3]=3=[r7c6]=6=[r7c1] -> r8c2<>6
Edited mistake, thanks to ronk

by **ronk** » Thu Apr 03, 2008 1:20 pm

eleven wrote:Would write it as
Either r7c8=4 or r5c8=4 -> r5c3=3 -> r5c9=1 -> r7c8=1, i.e. r7c8<>39

Edit: btw the second one gives a loop (with r7c8=1 -> r5c8=4), which also would allow to eliminate 6789 from r5c3 (r5c9<>1 -> r5c38=13) [corrected mistake]

You are correct about this being a continuous loop. However, I don't believe r5c9<>1 and r5c8<>4 are valid eliminations.

I again edited my original post here, this time to illustrate the continuous loop you noted. I also added a brief explanation of my nice loop notation for the ALS.

by **ronk** » Thu Apr 03, 2008 2:03 pm

eleven wrote:The "short version" would be enough:
6=[r8c2]=7=[r7c3]=3=[r7c6]=6=[r7c1] -> r7c1=6

Your implied complete nice loop is ..

[r7c1]=6=[r8c2]=7=[r7c3]=3=[r7c6]=6=[r7c1] -> r7c1=6

... but what of the candidate 6 in r8c1?

by **daj95376** » Thu Apr 03, 2008 3:54 pm

eleven wrote:Either r7c1=6 or r7c6=6 -> r7c3=3 -> r8c2=7 -> r2c2=6, i.e. r1c1<>6, r8c2<>6 [corrected typo]

Drop the part in red and you still have enough to crack the puzzle. Or, you could change your short version slightly.

6=[r8c2]=7=[r7c3]=3=[r7c6]=6=[r7c1]-6-[r8c2] -> [r8c2]<>6

by **eleven** » Thu Apr 03, 2008 4:49 pm

ronk wrote:
eleven wrote:The "short version" would be enough:
6=[r8c2]=7=[r7c3]=3=[r7c6]=6=[r7c1] -> r7c1=6

... but what of the candidate 6 in r8c1?

Thanks ronk, this was not my day. I found a mistake and typos myself in 2 posts, now you pointed out another mistake. Of course i only can say "-> r8c2<>6", but this also solves the puzzle.

ronk wrote:
eleven wrote:Would write it as
Either r7c8=4 or r5c8=4 -> r5c3=3 -> r5c9=1 -> r7c8=1, i.e. r7c8<>39

Edit: btw the second one gives a loop (with r7c8=1 -> r5c8=4), which also would allow to eliminate 6789 from r5c3 (r5c9<>1 -> r5c38=13) [corrected mistake]

You are correct about this being a continuous loop. However, I don't believe r5c9<>1 and r5c8<>4 are valid eliminations.

I did not mean here, that they can be eliminated, but that the implication r5c9<>1 -> r5c38=13 - together with r5c3=3 in the chain - allows to eliminate 6789 from r5c3 (see below)

I again edited my original post here, this time to illustrate the continuous loop you noted. I also added a brief explanation of my nice loop notation for the ALS.

Thanks for that. I think, i understand it now. It also shows an advantage of the notation. Its easier to see all possible eliminations from the loop.

Here is, how i would have to explain the same eliminations.

Code: Select all: +-----------------------------------------------------------------------------------------+ | 3689 1 2345689 | 7 34689 3689 | 289 2569 25689 | | 36789 26789 236789 | 2689 5 13689 | 4 1269 126789 | | 6789 2456789 256789 | 24689 1689 1689 | 12789 12569 3 | |-----------------------------+-----------------------------+-----------------------------| | 4 56789 156789 | 3 6789 25 | 1279 1269 12679 | | 2 6789 #136789 | 4689 6789 6789 | 5 #13469 #1679 | | 3679 5679 35679 | 1 4679 25 | 2379 8 24679 | |-----------------------------+-----------------------------+-----------------------------| | 5 4789 789 | 89 2 37 | 6 #1349 #189 | | 689 3 24689 | 5689 1689 1689 | 289 7 24589 | | 1 26789 26789 | 5689 37 4 | 2389 2359 2589 | +-----------------------------------------------------------------------------------------+

The eliminations were: r5c3<>6789, r5c8<>69, r24c9<>1 and r7c8=14

My loop was:
r5c8=4 -> r5c3=3 -> r5c9=1 -> r7c9<>1 -> r7c8=1 -> r5c8=4
Now i need the "opposite" loop (from right to left), one of them must be true:
r5c8<>4 -> r7c8=4 -> r7c9=1 -> r5c9<>1 -> r5c38=13 -> r5c8<>4
(note, that r5c9<>1 -> r5c3<>3 is not true, because r5c3=3 -> r5c9=1 depends on r5c8=4).

Now we have:
r5c3=3 or r5c3=13 -> r5c3=13 (the one i already had above)
r5c8=4 or r5c8=13 -> r5c8=134
r7c8=1 or r7c8=4 -> r7c8=14
r5c9=1 or r7c9=1 -> r24c9<>1

by **daj95376** » Thu Apr 03, 2008 10:54 pm

Code: Select all: ...3..71...6.5................1.73...85.........4......6..2...87.....4..1........ #44580 +--------------------------------------------------------------------------------------+ | 24589 2459 249 | 3 469 24689 | 7 1 24569 | | 2489 17 6 | 2789 5 12489 | 289 23489 2349 | | 24589 3 17 | 26789 14679 124689 | 25689 245689 24569 | |----------------------------+----------------------------+----------------------------| | 2469 249 249 | 1 689 7 | 3 245689 24569 | | 3469 8 5 | 269 369 2369 | 169 4679 14679 | | 2369 17 17 | 4 3689 5 | 2689 2689 269 | |----------------------------+----------------------------+----------------------------| | 459 6 349 | 579 2 1349 | 159 3579 8 | | 7 259 2389 | 5689 1369 13689 | 4 23569 123569 | | 1 2459 23489 | 56789 34679 34689 | 2569 235679 235679 | +--------------------------------------------------------------------------------------+

by **eleven** » Fri Apr 04, 2008 9:59 am

Nice puzzle for pencil&paper players ;)

Code: Select all: *----------------------------------------------------------------------* | 24589 2459 249 | 3 469 24689 | 7 1 24569 | | 2489 17 6 | 2789 5 12489 | 289 23489 2349 | | 24589 3 17 | 26789 #14679 124689 | 25689 245689 24569 | |---------------------+-----------------------+------------------------| | 2469 249 249 | 1 689 7 | 3 245689 24569 | | 3469 8 5 | 269 369 2369 | 169 4679 #14679 | | 2369 17 17 | 4 3689 5 | 2689 2689 269 | |---------------------+-----------------------+------------------------| | 459 6 349 | 579 2 1349 | 159 3579 8 | | 7 259 2389 | 5689 #1369 13689 | 4 23569 #123569 | | 1 2459 23489 | 56789 #34679 34689 | 2569 235679 #235679 | *----------------------------------------------------------------------*

There are 2 overlapping skyscrapers for 1 and 7, one of r3c5 and r5c9 must be 1 and one of them 7.
Then also one of r8c5 and r8c9 must be 1 and one of r9c5 and r9c9 is 7.
I.e. r3c5=17, r5c9=17, r8c6<>1, r9c48<>7

Code: Select all: *--------------------------------------------------------------------* |*24589 *2459 *249 | 3 #469 24689 | 7 1 24569 | |*2489 17 6 | 2789 5 12489 | 289 23489 2349 | |*24589 3 17 | 2689 17 24689 | 25689 245689 24569 | |---------------------+---------------------+------------------------| | 2469 249 249 | 1 689 7 | 3 245689 24569 | |#3469 8 5 | 269 369 2369 | 169 #4679 #17 | | 2369 17 17 | 4 3689 5 | 2689 2689 269 | |---------------------+---------------------+------------------------| | 459 6 349 | 579 2 1349 | 159 3579 8 | | 7 259 2389 | 5689 1369 3689 | 4 23569 123569 | | 1 2459 23489 | 5689 #34679 34689 | 2569 23569 #235679 | *--------------------------------------------------------------------*

Now to 4 an 7.
Skyscraper for 7 in rows 5 and 9, so one of r5c8 and r9c5 must be 7.
r5c8=7 -> r5c1=4 -> r1c23=4 -> r9c5=4
r9c5=7 -> r1c5=4 -> r23c1=4 -> r5c8=4
This also eliminates the 4's in r1c1, r1c69 and r47c1.
Then a ER eliminates 4 in r1c3.

Code: Select all: *-------------------------------------------------------------------* | 2589 2459 29 | 3 469 2689 | 7 1 2569 | | 2489 17 6 | 2789 5 12489 | 289 23489 2349 | | 24589 3 17 | 2689 17 24689 | 25689 245689 24569 | |---------------------+--------------------+------------------------| | 269 249 249 | 1 689 7 | 3 245689 24569 | | 3469 8 5 | 269 369 2369 | 169 47 17 | | 2369 17 17 | 4 3689 5 | 2689 2689 269 | |---------------------+--------------------+------------------------| | 59 6 349 | 579 2 1349 | 159 3579 8 | | 7 259 2389 | 5689 1369 3689 | 4 23569 123569 | | 1 2459 23489 | 5689 47 34689 | 2569 23569 235679 | *-------------------------------------------------------------------*

r5c9=1 -> r3c5=7 -> r9c5=4
r8c9=1 -> r7c6=1 -> r7c3=4
i.e. r7c6<>4, r9c23<>4

Code: Select all: *---------------------------------------------------------------* | 2589 459 29 | 3 469 2689 | 7 1 2569 | | 2489 17 6 | 2789 5 1289 | 289 23489 2349 | | 24589 3 17 | 2689 17 24689 | 25689 245689 24569 | |-----------------+--------------------+------------------------| | 269 49 29 | 1 689 7 | 3 245689 24569 | | 3469 8 5 | 269 369 2369 | 169 47 17 | | 2369 17 17 | 4 3689 5 | 2689 2689 269 | |-----------------+--------------------+------------------------| | 59 6 4 | 579 2 139 | 159 3579 8 | | 7 259 38 | 5689 1369 3689 | 4 23569 123569 | | 1 259 38 | 5689 47 34689 | 2569 23569 235679 | *---------------------------------------------------------------*

Either r5c9=1 or r5c9=7 -> r7c8=7 -> r7c6=3 -> r7c7=1, i.e. r5c7<>1

by **ronk** » Fri Apr 04, 2008 1:39 pm

eleven wrote:There are 2 overlapping skyscrapers for 1 and 7, one of r3c5 and r5c9 must be 1 and one of them 7.
Then also one of r8c5 and r8c9 must be 1 and one of r9c5 and r9c9 is 7.
I.e. r3c5=17, r5c9=17, r8c6<>1, r9c48<>7

Nice find. In nice-loop notation ...

r3c5 =1= r8c5 -1- r8c9 =1= r5c9 =7= r9c9 -7- r9c5 =7= r3c5 =1= continuous loop
==> r3c5=17, r5c9=17,r8c6<>1, r9c48<>7

by **daj95376** » Fri Apr 04, 2008 5:55 pm

Yes, nice find eleven! FWIW, your results match a forcing chain on [r3c3].

I ran into several 17s that looked difficult, and then discovered they had an Achille's Heel that cracked them in one advanced step. Of the difficult looking 17s that I did post, others were able to crack them with one advanced step as well.

Does this mean that I finally ran across a 17 (outside of gsf's list) that requires more than one advanced step to crack?

by **ronk** » Fri Apr 04, 2008 7:43 pm

daj95376 wrote:Does this mean that I finally ran across a 17 (outside of gsf's list) that requires more than one advanced step to crack?

Sure looks that way to me!

by **daj95376** » Sat Apr 05, 2008 1:06 am

As I mentioned earlier, eleven's results are equivalent to a forcing chain from [r3c3]. My (old) solver found a forcing net from [r3c3] that resulted in [r3c3]<>7. So, I kept looking for a way to extend the forcing chain from [r3c3] to produce a contradiction. I found it ... and then I found a shorter variant. Unfortunately, this results in one advanced step for this puzzle as well. Drat

Code: Select all: [r9c5]<>7 => simple SSTS solution to puzzle [r9c5]= 7 [r5c9]=7 [r8c9]=1 [r7c47]=59 [r7c1]=4 [r1c23]=4 [r3c5]=4 => [c5]~1

by **daj95376** » Sat Apr 05, 2008 6:16 am

This is the only other 17 with 62 unresolved cells (in the PM) that might take more than one advanced step.

Code: Select all: 2.......6.....1.3..5..4.....7...54..3...........6.....6..23....8..9...........1.. #26677 +--------------------------------------------------------------------------------------+ | 2 1348 13478 | 3578 5789 3789 | 578 14578 6 | | 479 4689 46789 | 578 26 1 | 25789 3 245789 | | 179 5 136789 | 378 4 26 | 2789 12789 12789 | |----------------------------+----------------------------+----------------------------| | 19 7 12689 | 138 289 5 | 4 2689 12389 | | 3 124689 124689 | 1478 2789 24789 | 256789 256789 125789 | | 5 12489 12489 | 6 2789 234789 | 23789 12789 123789 | |----------------------------+----------------------------+----------------------------| | 6 149 14579 | 2 3 478 | 5789 45789 45789 | | 8 234 2457 | 9 1 47 | 23567 24567 23457 | | 479 2349 23479 | 4578 5678 4678 | 1 2789 234789 | +--------------------------------------------------------------------------------------+

The New Sudoku Players' Forum

Contrary "17" Puzzles