The New Sudoku Players' Forum

by **daj95376** » Thu Apr 17, 2008 4:49 pm

Pat wrote:well, once we know where to look---
if r5c9=3
then r1c6=3, r1c8=7, r6c7=7, r6c9=2, r6c5=6,
conflict in r5: {2,6,7} must all fit in just 2 cells r5c13

Good point and nice solution!

Drat! I keep forgetting to look for conjugate cells. My (old) solver indicated that four of the five candidates in [r5c3] led to a contradiction using Singles in short networks. I just stayed with it and checked each for a usable chain.

by **daj95376** » Fri Apr 18, 2008 6:44 pm

This one looks like fun.

Code: Select all: ....2...18.4......3...........6.8.4..2....7.....3.....6..4...8..7..1.5........... #40423 +--------------------------------------------------------------------------------+ | 579 569 579 | 589 2 34569 | 34689 3569 1 | | 8 1569 4 | 1579 3569 135679 | 369 2 35679 | | 3 1569 2 | 15789 45689 14569 | 4689 5679 45679 | |--------------------------+--------------------------+--------------------------| | 1579 359 13579 | 6 579 8 | 1239 4 2359 | | 459 2 368 | 159 459 1459 | 7 36 368 | | 14579 48 56789 | 3 4579 2 | 169 1569 5689 | |--------------------------+--------------------------+--------------------------| | 6 359 1359 | 4 359 3579 | 1239 8 2379 | | 249 7 389 | 289 1 369 | 5 369 3469 | | 12459 48 13589 | 25789 35689 35679 | 13469 13679 34679 | +--------------------------------------------------------------------------------+

by **hobiwan** » Fri Apr 18, 2008 7:10 pm

daj95376 wrote:This one looks like fun.

Only if you are interested in solutions with 7 Nice Loops (plus 2 Remote Pairs) or as an alternative, 9 ALS moves

(that's the best my solver comes up with)

by **Draco** » Sat Apr 19, 2008 12:47 am

daj95376 wrote:This one looks like fun.

Code: Select all
....2...18.4......3...........6.8.4..2....7.....3.....6..4...8..7..1.5........... #40423

I'm able to get it down to 6 relatively short forcing chains interspersed with STSS to solve. Not pretty but a bit shorter than hobiwan...

Cheers...

- drac

by **eleven** » Sat Apr 19, 2008 5:23 pm

Those last puzzles were a bit too hard for my taste. After long tries i found a solution with 4 chains.
The first eliminated 4 in r8c1:
Either r8c1=2 or (r8c4=2 -> r8c3=8 -> r9c2=4)

Code: Select all: *-----------------------------------------------------------------------------* | 579 569 579 | 589 2 #34569 | 48 #3569 1 | | 8 1569 4 | 1579 3569 135679 | 369 2 35679 | | 3 1569 2 | 15789 45689 14569 | 48 5679 5679 | |-------------------------+-------------------------+-------------------------| | 1579 359 13579 | 6 579 8 | 1239 4 2359 | | 459 2 368 | 159 459 1459 | 7 *36 368 | | 14579 48 56789 | 3 4579 2 | 169 1569 5689 | |-------------------------+-------------------------+-------------------------| | 6 359 1359 | 4 359 3579 | 1239 8 2379 | | 29 7 389 | 289 1 #369 | 5 #369 4 | | 12459 48 13589 | 25789 35689 35679 | 1369 13679 3679 | *-----------------------------------------------------------------------------*

Here from r5c8=36 you get:
Either r1c6=3 or r8c6=6, i.e. r1c6<>6 and r8c6<>3. This gives a strong link for 3 in r8.

Code: Select all: *-----------------------------------------------------------------------------* | 579 569 579 |#589 2 @34-59 |#48 @3569 1 | | 8 1569 4 | 1579 3569 135679 | 369 2 35679 | | 3 1569 2 | 15789 45689 14569 | 48 5679 5679 | |-------------------------+-------------------------+-------------------------| | 1579 359 13579 | 6 579 8 | 1239 4 2359 | | 459 2 368 | 159 459 1459 | 7 -36 368 | | 14579 48 56789 | 3 4579 2 | 169 1569 5689 | |-------------------------+-------------------------+-------------------------| | 6 359 1359 | 4 359 3579 | 1239 8 2379 | | 29 7 #@389 |#289 1 69 | 5 @369 4 | | 12459 48 13589 | 25789 35689 35679 | 1369 1-3679 3679 | *-----------------------------------------------------------------------------*

Now the kite for 8 and the skyscraper for 3 are connected by a strong link for 4 in r1.
This gives a cycle with eliminations:
r1c6<>59, r59c8<>3, r8c3<>9, r39c4<>8
But still it doesn't solve it.

Code: Select all: *--------------------------------------------------------------------* | 579 6 579 | 589 2 @34 | 48 @359 1 | | 8 159 4 | 1579 3569 13579 | 369 2 35679 | | 3 159 2 | 1579 45689 1459 | 48 579 5679 | |----------------------+----------------------+----------------------| | 1579 359 1579 | 6 579 8 | 1239 4 2359 | | 459 2 38 | 159 459 1459 | 7 6 38 | | 14579 48 6 | 3 4579 2 | 19 159 589 | |----------------------+----------------------+----------------------| | 6 359 159 | 4 359 3579 | 1239 8 279 | | 29 7 #38 | 289 1 6 | 5 @39 4 | | 12459 #48 159 | 2579 #@3589 *3579 |*1369 179 679 | *--------------------------------------------------------------------*

r8c8=3 eliminates 3 in both r9c67 -> r9c5=3 -> r9c2=8 -> r8c3=3

by **daj95376** » Sat Apr 19, 2008 6:27 pm

eleven wrote:Those last puzzles were a bit too hard for my taste.

Yes, I went too far in my search for puzzles that present a challenge while still being fun. The last couple of puzzles weren't fun. I'll try to rectify this shortcoming in my next posts.

What I did find interesting is that everyone (seems to) look for eliminations and misses/ignores common assignments. On the last puzzle, a forcing chain assignment results in several eliminations and exposes a Hidden Pair for several more eliminations. After that, a couple of long forcing chains help, but I subsequently lost interest.

Code: Select all: [r9c2]=4 [r8c9]=4 [r9c2]=8 [r8c368]=369 [r8c9]=4 c7 - 48 Hidden Pair [r6c2]=4 [r9c2]=8 [r8c4]=8 [r1c7]=8 [r1c6]=4 ... [r1c8]=3 [r5c8]=6 [r8c8]=9 [r8c3]=3 [r5c3]=8 => [r5c9]<>6 [r6c3]<>8 [r6c2]=8 [r5c9]=8 => [r5c9]<>6 [r6c3]<>8 [r3c7]=4 [r1c6]=4 [r1c8]=3 [r5c8]=6 [r8c8]=9 ... [r8c1]=2 [r8c4]=8 [r8c3]=3 [r5c3]=8 => [r3c4]<>8 [r9c34]<>8 [r3c7]=8 [r1c4]=8 [r9c5]=8 => [r3c4]<>8 [r9c34]<>8

Yes, carrying the forcing chain assignments one step further would result in common eliminations, but where's the fun in that?

by **hobiwan** » Sun Apr 20, 2008 8:32 pm

daj95376 wrote:Yes, I went too far in my search for puzzles that present a challenge while still being fun. The last couple of puzzles weren't fun. I'll try to rectify this shortcoming in my next posts.

Don't be too hard on yourself, after all it's you who does most of the work by choosing the puzzles for us to have fun. I think a big Thank You is in order (and I am looking forward to whatever you will throw at us)

by **daj95376** » Mon Apr 21, 2008 1:24 am

Thanks hobiwan for the kind words. I do what I can with what I currently have at hand.

I decided to skip these three 17/61s because they seemed to lack the fun aspect. You may have a different opinion.

Code: Select all: ....3...2..6...5...1.4...........16.....8..4.2.....3.....7.6...3.......5...1..... # 3661 ....3...26.....5...1.7.........524...74...........1......8...1.2.3......5........ #40762 ....3...26.....5...1.4.........527...74...........1......8...1.2.3......5........ #40763

This one looks complicated, but it has an Achilles Heel that shouldn't be too difficult to find.

Code: Select all: ...2.7..4.3.5.....6.....9..15..4.....2.....7.......3..8...6.......7...5.......... # 7910 *--------------------------------------------------------------------------------------* | 59 189 189 | 2 1389 7 | 1568 1368 4 | | 2479 3 12489 | 5 189 6 | 1278 128 1278 | | 6 178 1258 | 1348 138 1348 | 9 1238 123578 | |----------------------------+----------------------------+----------------------------| | 1 5 7 | 3689 4 2389 | 268 2689 2689 | | 349 2 34689 | 1689 158 189 | 14568 7 1689 | | 49 4689 4689 | 1689 7 12589 | 3 124689 125689 | |----------------------------+----------------------------+----------------------------| | 8 1479 123459 | 1349 6 13459 | 1247 12349 12379 | | 2349 1469 123469 | 7 1238 13489 | 12468 5 123689 | | 234579 14679 123469 | 13489 12358 13489 | 124678 1234689 123689 | *--------------------------------------------------------------------------------------*

by **hobiwan** » Mon Apr 21, 2008 6:54 am

#7910:

I am not down to one move, but I have two Nice Loops, that together eliminate 17 candidates:

Continuous Nice Loop [r1c1]-9-[r6c1]-4-[r6c8]=4=[r5c7]=5=[r1c7]-5-[r1c1] => [r5c7]<>168, [r6c23]<>4, [r2589c1]<>9
Locked Candidates Type 2 (Claiming): 4 in c2 => [r789c3],[r89c1]<>4
Continuous Nice Loop [r5c1]-3-[r8c1]-2-[r8c5]=2=[r9c5]=5=[r5c5]-5-[r5c7]-4-[r5c1] => [r9c5]<>1, [r8c379]<>2, [r9c15]<>3, [r5c3]<>4, [r9c5]<>8

After that another chain solves the puzzle:
Discontinuous Nice Loop [r7c3]=5=[r3c3]=2=[r2c1]=7=[r9c1]=5=[r7c3] => [r7c3]<>1, [r7c3]<>2, [r7c3]<>3, [r7c3]<>9

by **eleven** » Mon Apr 21, 2008 4:53 pm

daj95376 wrote:This one looks complicated, but it has an Achilles Heel that shouldn't be too difficult to find.

This solves it:
r3c9=7 -> r3c3=5 -> r1c1=9 -> r1c23=18 -> r3c2=7

by **daj95376** » Mon Apr 21, 2008 6:05 pm

With the right (wrong?) selection in [c1], a subset count contradiction results in [b1]:

Code: Select all: [r1c1]=9 [r6c1]=4 [r5c1]=3 [r8c1]=2 [r23c3]=245; => [r1c1]<>9

by **eleven** » Tue Apr 22, 2008 3:10 pm

daj95376 wrote:I decided to skip these three 17/61s because they seemed to lack the fun aspect. You may have a different opinion.

Code: Select all
....3...2..6...5...1.4...........16.....8..4.2.....3.....7.6...3.......5...1..... # 3661 ....3...26.....5...1.7.........524...74...........1......8...1.2.3......5........ #40762 ....3...26.....5...1.4.........527...74...........1......8...1.2.3......5........ #40763

At least its interesting, that they can be solved with the same trick:
Take a skyscraper and look, what you can do with the pincers.

Code: Select all: *---------------------------------------------------------------------* | 45789 45789 45789 | 5689 3 15789 | 46789 1789 2 | |*4789 23 6 | 289 1279 12789 | 5 13789 #134 | | 5789 1 23 | 4 2679 25789 | 6789 3789 36 | |--------------------------+---------------------+--------------------| | 45789 345789 345789 | 2359 2479 24579 | 1 6 789 | |#15679 35679 13579 | 3569 8 1579 | 2 4 79 | | 2 46789 14789 | 69 14679 1479 | 3 5 789 | |--------------------------+---------------------+--------------------| |#14589 24589 124589 | 7 2459 6 | 489 12389 #134 | | 3 24679 12479 | 289 249 2489 | 4679 1279 5 | |*456789 2456789 245789 | 1 2459 3 | 46789 2789 *46 | *---------------------------------------------------------------------*

Skysrcaper for 1, either r2c9=1 or r5c1=1.
r2c9=1 -> r2c1=4
r5c1=1 -> r9c1=6 -> r9c9=4
i.e. r2c9<>4, r9c1<>4

Second puzzle:

Code: Select all: *--------------------------------------------------------------------* | 4789 459 5789 |#1569 3 45689 |*16789 46789 2 | | 6 2349 2789 | 129 12489 489 | 5 34789 134789 | | 3489 1 2589 | 7 24689 45689 | 3689 34689 34689 | |-------------------+---------------------+--------------------------| | 1389 369 689 | 39 5 2 | 4 3789 13789 | | 139 7 4 | 369 689 3689 |*1239 #2359 1359 | | 389 25 25 | 4 7 1 | 3689 3689 3689 | |-------------------+---------------------+--------------------------| | 479 469 679 | 8 2469 34569 | 2369 1 34569 | | 2 4689 3 |#1569 1469 45679 | 6789 #456789 456789 | | 5 4689 1 | 2369 2469 34679 | 236789 2346789 346789 | *--------------------------------------------------------------------*

Skysrcaper for 5, either r1c4=5 or r5c8=5.
r1c4=5 -> r1c7=1
r5c8=5 -> r5c7=2
i.e. r5c7<>1

Code: Select all: *------------------------------------------------------------------* | 4789 459 5789 | 569 3 45689 | 1 46789 2 | | 6 2349 2789 |#129 12489 489 | 5 34789 34789 | | 3489 1 2589 | 7 24689 45689 | 3689 34689 34689 | |-------------------+---------------------+------------------------| | 1389 369 689 | 39 5 2 | 4 3789 13789 | | 139 7 4 | 369 689 3689 | 239 #2359 1359 | | 389 25 25 | 4 7 1 | 3689 3689 3689 | |-------------------+---------------------+------------------------| | 479 469 679 | 8 2469 34569 | 2369 1 34569 | | 2 4689 3 |*1569 1469 45679 | 6789 *45689 45689 | | 5 4689 1 |#2369 2469 34679 | 236789 #234689 34689 | *------------------------------------------------------------------*

Skysrcaper for 2, either r2c4=2 or r5c8=2.
r2c4=2 -> r8c4=1
r5c8=2 -> r8c8=5
i.e. r8c4<>5

The third puzzle solves exactly the same way (only differs in 2 4-7 changes).

by **daj95376** » Mon Apr 28, 2008 4:33 am

I could not get this one to cooperate. However, it should give hobiwan some forcing chains to investigate.

Code: Select all: .4..1..........5.6......3..5.38.....7......2..........6..5.7....2.....1....3..4.. #39462 +--------------------------------------------------------------------------------------+ | 389 4 56789 | 679 1 35689 | 2789 789 2789 | | 12389 13789 12789 | 2479 34789 3489 | 5 4789 6 | | 289 56789 256789 | 24679 456789 45689 | 3 4789 1 | |----------------------------+----------------------------+----------------------------| | 5 169 3 | 8 4679 2 | 1679 679 479 | | 7 1689 14689 | 1469 34569 34569 | 1689 2 34589 | | 12489 1689 124689 | 14679 35679 469 | 16789 356789 35789 | |----------------------------+----------------------------+----------------------------| | 6 1389 1489 | 5 2489 7 | 289 389 2389 | | 3489 2 45789 | 469 4689 4689 | 6789 1 35789 | | 89 5789 5789 | 3 2689 1 | 4 56789 25789 | +--------------------------------------------------------------------------------------+

by **Draco** » Mon Apr 28, 2008 7:23 am

daj95376 wrote:I could not get this one to cooperate. However, it should give hobiwan some forcing chains to investigate.

Code: Select all
.4..1..........5.6......3..5.38.....7......2..........6..5.7....2.....1....3..4.. #39462

That was a mouthful; from your PM's my solver needed 7 (fairly short) FC's for STSS to solve; the last one is really a Forcing Net but still a simple one. I'd be happy to transcribe 'em if you want to see the list -- well perhaps happy is the wrong word... ;) but certainly willing.

Cheers...

- drac

by **hobiwan** » Mon Apr 28, 2008 8:30 am

#39462:
It is funny how much the difficulty of a sudoku depends on the techniques used (and their order). This is one my solver had no problems with (even without Forcing Chains). A possible solution:

Code: Select all: Continuous Nice Loop [r1c1]=3=[r1c6]=5=[r1c3]-5-[r8c3]=5=[r8c9]=3=[r8c1]-3-[r1c1] => [r2c1]<>3, [r39c3]<>5, [r1c6]<>689, [r8c9]<>789 Discontinuous Nice Loop [r8c9]-3-[r7c8]=3=[r6c8]=5=[r9c8]=6=[r8c7]=7=[r8c3]=5=[r8c9] => [r8c9]<>3 Singles (plus 1 Finned Jellyfish)

But you are right, lots of Forcing Chains!

The New Sudoku Players' Forum

Contrary "17" Puzzles

Re: re: # 2919