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by **ravel** » Fri May 19, 2006 2:57 pm

ronk wrote:Would someone please tell me how to get past this point?

This is my solution. Points 3 and 6 are rather complicated.

After the swordfish in 8 r479c357 => r479c28<>8, r9c9<>8:
[edited typo]
1.r4c3=8 => r6c8=8 => r2c9=8 => r2c2=2 => no 2 for col3 => r6c2=8
2.
r6c8=9 => r6c1=5
r6c8=9 => r5c7=7 => r5c9=3 => r5c3=5
=> r5c7=9
Brings us here with an type 4 UR 68 in r79c35 (r79c3<>6)

Code: Select all: 3567 9 23456 | 8 17 24 | 2567 1357 2367 57 257 1 | 6 3 9 | 4 578 278 8 23457 23456 | 5 17 24 | 267 137 9 ------------------------------------------------------------------------- 4 123 23 | 17 9 6 | 8 37 5 135 6 35 | 17 4 8 | 9 2 37 9 8 7 | 2 5 3 | 1 6 4 ------------------------------------------------------------------------- 2 3457 3458 | 39 68 57 | 567 49 1 567 57 9 | 4 2 1 | 3 578 678 13567 13457 3458 | 39 68 57 | 2567 49 267

----
3.
r4c2=1 => r9c2<>1
r4c2=1 => r4c4=7 => r3c8=3 => r1c9=3 => r13c7=6 => r79c6<>6 => (AUR 57 in r79c67)r9c7=2 => r2c9=2 => r28c2=57
=> r79c2=34 => deadly pattern 34/39/49 in r79c248
=> r5c1=1
4. ER in 5: r28c8,box 1 => r8c1<>5 => r8c1=6
5. xy-chain: 7-r8c2-5-r8c8-8-r2c8-5-r1c2-7 => r89c1<>7,r23c2<>7
6.
r9c1=5 => r1c1=3 => r1c8=1 => r1c5=7
r9c1=5 => r2c1=7,r2c2=5 => r2c8=8 => r2c9=2 => r1c7=2 (=> r9c9<>2)
r9c1=5 => r9c6=7 => r9c9=6
=> r1c9 is empty => r9c1=3

by **gsf** » Fri May 19, 2006 3:13 pm

ravel wrote:
ronk wrote:Would someone please tell me how to get past this point?

This is my solution. Points 3 and 6 are rather complicated.

After the swordfish in 8 r479c357 => r479c28<>8, r9c9<>8:
1.r4c3=8 => r6c8=8 => r2c9=8 => r2c2=2 => no 2 for col3 => r5c2=8

something's amiss
[52]=6 is a clue from ronk's pencilmarks

by **ravel** » Sat May 20, 2006 9:55 am

gsf wrote:[52]=6 is a clue from ronk's pencilmarks

Thanks, should be r6c2=8, i correct it above.

by **Karlson** » Thu Jun 01, 2006 9:31 pm

This one should not be too hard but is interesting:
#7:

Code: Select all: 8...........3..92.....21..5..8.1...7.6.5..1...9..3.2.65..8.......4..3.6...1..6..9

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

by **Karlson** » Fri Jun 02, 2006 11:35 am

This one is #276 from Into Sudoku - posted by Scott. Into Sudoku needs many forcing chains and has to guess 4x:
#8

Code: Select all: ...86..1.7....1..5......8..2...1.7.81......4..5.7.4..9.73.....6.2...5...6....9..7

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

by **ravel** » Fri Jun 02, 2006 12:16 pm

I also needed 4 steps, will add it to my list

by **Carcul** » Tue Jun 06, 2006 8:57 am

Here is a possible solution for Puzzle #4:

Code: Select all: *--------------------------------------------------------------------* | 2 3 5689 | 5679 1456 46789 | 1459 1456 469 | | 5689 568 1 | 3569 2 34689 | 459 3456 7 | | 7 4 569 | 3569 1356 369 | 8 12356 2369 | |----------------------+----------------------+----------------------| | 4 568 35678 | 236 9 1 | 25 2357 23 | | 369 2 3679 | 4 36 5 | 19 137 8 | | 359 1 359 | 8 7 23 | 6 2345 2349 | |----------------------+----------------------+----------------------| | 356 7 23456 | 1 8 2346 | 24 9 246 | | 1 68 2468 | 79 46 79 | 3 2468 5 | | 368 9 23468 | 2356 3456 2346 | 7 2468 1 | *--------------------------------------------------------------------*

1. [r6c6]-3-[r7c6|r8c5|r9c6]-2-[r6c6], => r2c6/r3c6<>3.

2. [r6c9]-2/3-[r3c6|r34c9]-6,9-[r3c3]-5-[r2c2]=5=[r4c2](-5-[r4c7]-2-
[r6c9])-5-[r6c13]-3-[r6c9], =>r6c9<>2,3.

3. [r4c4]-3-[r2c4]=3=[r2c8]-3-[r3c9]=3=[r4c9]-3-[r4c4], => r4c4<>3.

4. [r7c6]-2-[r7c7]=2=[r4c7]-2-[r4c4]=2=[r6c6]-2-[r7c6], => r7c6<>2.

5. [r5c8]-3-[r5c5]-6-[r4c4]-2-[r4c9]-3-[r5c8], => r5c8<>3.

6. [r6c6](-3-[r5c5]-6-[r8c5]-4-[r7c6])-3-[r6c13](-9-[r6c9]-4-[r7c9])-5-
[r4c2]=5=[r2c2]-5-[r3c36]-6,9-[r34c9]-2-[r7c9]-6-[r7c6]-3-[r6c6],
=> r6c6<>3.

7. [r1c5]-1-[r1c78]=1=[r3c8]-1-[r5c8]-7-[r5c3]=7=[r4c3]=8=[r4c2]=
=5=[r2c2]-5-[r3c3]=5|1=[r3c5]-1-[r1c5], => r1c5<>1.

8. [r1c9]-6-[r1c5]=6=[r8c5](-6-[r8c8])-6-[r8c2]-8-[r7c7|r8c8]-2,4-[r7c9]-
-6-[r1c9], => r1c9<>6.

9. [r4c8]=7=[r5c8]=1=[r5c7]=9=[r6c9]=4=[r6c8]-4-[r89c8]=4=[r7c7]=
=2=[r4c7](-2-[r4c8])-2-[r4c9]-3-[r4c8], => r4c8<>2,3.

10. [r1c46]-9-[r1c9]-4-[r1c5]-6-[r3c6]-9-[r1c46], => r1c4/r1c6<>9.

11. [r2c8](-3-[r3c9]=3=[r4c9]=2=[r4c7]-2-[r7c7]-4-[r2c7])-3-
[r2c47](-5-[r2c2]=5=[r4c2]-5-[r6c1])-5,9-[r2c12]=5,9=[r13c3]-5,9-[r6c3]
-3-[r6c1]-9-[r6c9]=9=[r1c9](-9-[r2c7])-9-[r1c3]-5-[r1c4]-7-[r8c4]
-9-[r2c4]-5-[r2c7], => r2c8<>3.

12. [r2c8]-5-[r2c2]=5=[r4c2]-5-[r6c13]=5=[r6c8]-5-[r2c8], => r2c8<>5.

13. [r2c1]-5-[r7c1]=5=[r7c3]=2=[r7c7]-2-[r4c7]-5-[r4c2]=5=[r2c2]-
-5-[r2c1], => r2c1<>5.

14. [r1c7]=1=[r5c7]=9=[r6c9]=4=[r1c9]-4-[r1c7], => r1c7<>4.

15. [r7c6]=3=[r9c6]=6=[r8c5]-6-[r8c2]=6=[r2c2]=5=[r2c7]=4=[r7c7]-
-4-[r7c6], => r7c6<>4.

16. [r9c1]=3=[r6c1]-3-[r6c8]=3=[r4c9]=2=[r4c7]-2-[r7c7]-4-[r9c8]-
-8-[r9c1], => r9c1<>8.

17. [r5c1]=6=[r5c3]=7=[r5c8]=1=[r5c7]=9=[r6c9]=4=[r1c9]-4-[r1c5]=
=4=[r8c5]=6=[r9c6]-6-[r9c1]=6=[r5c1], => r5c1=6 which solve the puzzle.

Carcul

by **Carcul** » Tue Jun 06, 2006 12:37 pm

A possible solution for Puzzle #2.

This puzzle allows some interesting applications of the TILA (Two Incompatible Loops Argument) and of the corresponding Almost TILA (ATILA). This post explains the TILA.

Code: Select all: *----------------------------------------------------------* | 2349 23469 8 | 79 147 1349 | 479 5 14679 | | 7 49 5 | 6 2 149 | 8 3 149 | | 1 3469 469 | 5789 478 3459 | 2 469 4679 | |---------------------+------------------+-----------------| | 349 34789 49 | 1 5 2 | 6 489 479 | | 259 12589 129 | 4 6 7 | 3 189 25 | | 245 124567 1246 | 3 9 8 | 47 14 25 | |---------------------+------------------+-----------------| | 2459 12459 3 | 2589 148 14569 | 49 7 4689 | | 6 459 7 | 589 3 459 | 1 2 489 | | 8 1249 1249 | 279 147 1469 | 5 469 3 | *----------------------------------------------------------*

1. Type-3 Unique Rectangle in cells [r56c19|r4c3].

2. [r4c8]=8=[r5c8]=9=[r5c1]-9-[r4c3]-4-[r4c8], => r4c8<>4.

3. [r56c1]-2-[r1c1]=2|6=[r3c3]-6-[r56c3]-2-[r56c1], => r5c1/r6c1<>2.

4. [r9c5](-1-[r7c5])(-1-[r9c23]=1|5=[r8c2]-5-[r8c4])-1-[r1c457]-4,9-
[r1c1]-2-[r7c17]-4-[r7c5]-8-[r8c4]-9-[r1c4]-7-[r9c4]=7=[r9c5],
=> r9c5<>1.

5. =5=[r7c6](-5-[r8c4])=6=[r9c6](-6-[r9c8]=6=[r3c8]-6-[r1c9|r3c3])=1=
[r7c5]-1-[r1c457]-4,7,9-[r1c9]-1-[r2c9]=(ATILA: r2c2|r3c3|r4c3|r4c9|
|r2c9)=1|7=[r4c9]-7-[r6c7]=7=[r1c7]-7-[r1c4]-9-[r8c4]-8-[r8c9]=8=
=[r7c9]=6=[r7c6], => r7c6<>5.

6. [r3c2]=3=[r3c6]=5=[r8c6]-5-[r28c2]-4,9-[r3c2], => r3c2<>4,9.

7. [r1c6]=3=[r1c2](=2=[r1c1]-2-[r7c1])-3-[r3c2](-6-[r3c9])-6-[r3c38]-
-4,9-[r3c9]-7-[r4c9]=7=[r6c7]-7-[r1c7]-{TILA: r3c3|r4c3|r6c1|r7c1|r7c7|
|r1c7|r3c8}, => r1c2<>3.

8. =7=[r1c9](-7-[r1c7]=7=[r6c7])=6=[r1c2](=2=[r1c1]-2-[r7c1])-6-
-[r3c3]=(ATILA: r3c3|r4c3|r6c1|r7c1|r7c7|r1c7|r3c8)=6=[r3c8]-6-[r3c9]-
-(ATILA: r3c3|r4c3|r6c1|r7c1|r7c7|r1c7|r3c9)-7-[r1c9], => r1c9<>7.

9. [r9c6]-1-[r9c23]=1=[r7c2]=5=[r7c4]=2=[r9c4]-2-[r9c23]=2=[r7c1]-
-2-[r1c1]=2=[r1c2]=6=[r3c3](-6-[r3c8]=6=[r9c8])-6-[r6c3]=6=[r6c2]=
=7=[r6c7]-7-[r1c7]-{TILA:r1c1|r1c7|r3c8|r6c8|r4c9|r4c3|r9c3|r9c2|r2c2}
=> r9c6<>1.

10. [r1c9]=1=[r1c5]-1-[r7c5]=1=[r7c6]=6=[r7c9]-6-[r1c9], => r1c9<>6.

11. [r6c7](-7-[r1c7])-7-[r4c9]=(ATILA: r2c9|r2c2|r3c3|r4c3|r4c9)=7|1=
=[r2c9]-1-[r1c9]-{TILA: r1c7|r1c9|r4c9|r4c3|r6c1|r7c1|r7c7},
=> r6c7<>7 and that solves the puzzle.

Carcul

by **ravel** » Tue Jun 06, 2006 2:23 pm

Very sophisticated again.

I was curious about (A)TILA and read the first 7 steps.
Is it correct, that the ATILA in step 5 is a 49 remote pair and the TILA in step 7 a deadly bivalue/bilocation loop for number 4 (r6c1 containing 45, the rest 49) ?
If so, is it possible, that you denote in some way, what we can find in the (A)TILA ?

by **Carcul** » Tue Jun 06, 2006 4:40 pm

Thanks.

Ravel wrote:Is it correct, that the ATILA in step 5 is a 49 remote pair

You can see it in that way, but it is easier to see it (for me) as an Almost Deadly Turbot Fish.

Ravel wrote:and the TILA in step 7 a deadly bivalue/bilocation loop for number 4 (r6c1 containing 45, the rest 49) ?

Yes, correct. For every cell C of that deadly pattern we can write two loops, one that forces C = 4 and another that implies C<>4: a contradiction situation.

Ravel wrote:If so, is it possible, that you denote in some way, what we can find in the (A)TILA ?

Yes. In this case, as every TILA is due to incompatible X-cycles on "4", it could be written "{TILA(4): ...}". In other cases where the TIL's are more complicated nice loops, I write "{TILA(x): (1); (2)}", where (1) and (2) are the two incompatible loops written in the known notation. How does that sound to you (and the others users)?

by **daj95376** » Tue Jun 06, 2006 4:46 pm

Puzzle #2: Scanning cells in descending order and only using exposed Naked/Hidden Singles in chains.

Code: Select all: r4c5 = 5 Naked Single r4c6 = 2 Naked Single r5c5 = 6 Naked Single r9c9 = 3 Hidden Single r5c7 = 3 Hidden Single b3 - 1 Locked Candidate (1) b9 - 8 Locked Candidate (1) c9 - 25 Hidden Pair r9c8 = 6 [r9c8]=4 => [r7c6]=EMPTY ; [r9c8]=9 => [r7c1]=EMPTY r7c6 = 6 Hidden Single r7c7 = 9 [r7c7]=4 => [r5c8]=EMPTY c9 - 48 Naked Pair r1c7 ~ 9 XY-Wing r4c9 ~ 4 XY-Wing r6 - 25 Naked Pair r6c8 = 1 [r6c8]=4 => [r8c2]=EMPTY r6c3 = 6 Naked/Hidden Singles complete puzzle

Since I don't currently suport Uniqueness Rectangles, one of my steps above might be replaced by it -- as per Carcul.

by **ravel** » Tue Jun 06, 2006 5:02 pm

Carcul wrote:Yes. In this case, as every TILA is due to incompatible X-cycles on "4", it could be written "{TILA(4): ...}". In other cases where the TIL's are more complicated nice loops, I write "{TILA(x): (1); (2)}", where (1) and (2) are the two incompatible loops written in the known notation. How does that sound to you (and the others users)?

Yes, good, it would be easier to follow then (sometimes i am not sure, if i still have the same candidates after some steps).

by **Carcul** » Tue Jun 06, 2006 5:50 pm

A possible solution for Puzzle #6:

Code: Select all: *---------------------------------------------------------------* | 35679 234579 23456 | 8 157 2457 | 2567 13567 2367 | | 57 257 1 | 6 3 9 | 4 578 278 | | 8 23457 23456 | 257 157 2457 | 2567 13567 9 | |----------------------+-----------------+----------------------| | 4 1238 238 | 127 9 267 | 678 3678 5 | | 1359 6 35 | 157 4 8 | 79 2 37 | | 59 2589 7 | 25 56 3 | 1 689 4 | |----------------------+-----------------+----------------------| | 2 34578 34568 | 39 5678 567 | 56789 456789 1 | | 567 578 9 | 4 2 1 | 3 5678 678 | | 13567 134578 34568 | 39 5678 567 | 256789 456789 2678 | *---------------------------------------------------------------*

1. [r2c9]=8=[r2c8](-8-[r8c8])-8-[r6c8]=8=[r6c2]-8-[r8c2]=8=[r8c9]-8-
-[r2c9], => r479c28/r9c9<>8.

2. [r6c8]-8-[r4c7]=8=[r4c3]=2=[r4c2]-2-[r2c2]=2=[r2c9]=8=[r2c8]-8-
-[r6c8], => r6c8<>8.

3. [r13c5]-5-[r6c5]-6-[r4c6]=6=[r4c8]=3=[r5c9]-3-[r5c3]-5-[r5c4]=5=
=[r3c4]-5-[r13c5], => r1c5/r3c5<>5.

4. [r9c2]=1=[r9c1]-1-[r5c1]=1=[r5c4]=7=[r5c9]=3=[r1c9]-3-[r13c8]=
=(AUR: r13c58)=3|5=[r1c8]-5-[r28c8]=5=[X-Wing: r28c12]-5-[r9c2|r5c1]
=> r9c2/r5c1<>5.

5. [r5c1]=1=[r9c1]-1-[r9c2]=(AUPattern: r79c248/r8c2)=1|5,7=[r789c2]
(-5,7-[r2c2]-2-[r2c9])-5,7-[r8c1]-6-[r8c9]=(AUR: r28c89)=6|5=[r28c8]-
-5-[r1c8]=(AUR: r13c58)=5|3=[r13c8]-3-[r1c9]=3=[r5c9]-3-[r5c1],
=> r5c1<>3.

6. [r1c1]=5=[r1c7]-5-[r2c8]=5=[r8c8](-5-[r8c1]-5-[r1c1])=8=[r8c9]=6=
[r8c1]-6-[r1c1], => r1c1<>6; r8c1<>5.

7. [r23c2]-7-[r8c2]-5-[r8c8]-8-[r8c9]=8=[r2c9]=2=[r2c2]=7=[r2c1]-7-
-[r3c2], => r2c2/r3c2<>7.

8. [r3c7]=7=[r3c5]=1=[r3c8]=3=[X-Wing: r34c23](-3-[r9c3])-3-[r7c23]
=3=[r7c4]-3-[r9c4]-9-[r9c8]-4-[r9c3]-8-[r7c3]=8=[r7c5]=6=[r7c7]-6-
-[r3c7], => r3c7<>6.

9. [r9c9]-6-[r7c7]=6=[r7c5]=8=[r7c3]-8-[r9c348]-3-[r9c1]=3=[r1c1]=5=
=[r1c7](-5-[r7c7])=6=[r1c9]-6-[r9c9], => r9c9<>6; r7c7<>5.

10. [r9c9]=2=[r2c9]-2-[r2c2]-5-[r12c1]=5=[r9c1]-5-[r9c6]-7-[r9c9],
=> r9c9<>7 and that solves the puzzle.

Carcul

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