The New Sudoku Players' Forum

by **udosuk** » Thu Mar 08, 2007 8:44 pm

I'm not sure if Sudoku X puzzles is appropriate in here... If not please tell me...

This is the pencilmark grid:

Code: Select all: *--------------------------------------------------------------------------------------* | 4 1 5 | 23 23 6 | 7 8 9 | | 9 6 23 | 78 78 4 | 23 1 5 | | 7 28 238 | 5 9 1 | 23 4 6 | |----------------------------+----------------------------+----------------------------| | 8 4 17 | 137 6 37 | 5 9 2 | | 2 3 17 | 1789 5 789 | 18 6 4 | | 5 9 6 | 248 1248 28 | 18 3 7 | |----------------------------+----------------------------+----------------------------| | 13 5 248 | 6 123478 2378 | 9 27 138 | | 13 278 2489 | 1234789 123478 5 | 6 27 138 | | 6 278 289 | 123789 12378 23789 | 4 5 138 | *--------------------------------------------------------------------------------------*

I've managed to solve it using a variety of diagonal turbot fish moves and then a forcing chain which is a bit too long to my liking... Anybody know any better way?

Uniqueness-based moves are acceptable, though you need to be extra careful... For example if you carelessly apply the UR-type 1 in r23c37, then you'll run into trouble... Because of the diagonals it's not a genuine UR...

by **Steve R** » Fri Mar 09, 2007 2:10 pm

I think this works:

Eliminate 3 from r9c9 using the conjugate pairs (r3c3, r3c7) and (r4c4, r4c6)
Eliminate 4 from r8c5 using the conjugate pairs (r6c4, r6c5) and (r7c3, r7c5)
Eliminate values using the pair (49) in row 8, columns 3 and 4
Eliminate 7 from r8c5 using the conjugate pairs (r2c4, r2c5) and (r4c4, r8c8)
Eliminate 7 from r9c4 using the conjugate pairs (r8c2, r9c2) and (r4c4, r8c8)
Eliminate 7 from r7c6 using the conjugate pairs (r4c6, r8c2) and (r7c8, r8c8)
Eliminate values using the pair (2S) in column 6, rows 6 and 7
Eliminate 2 from r7c3 and r7cS using the conjugate pairs (r6c6, r7c6) and (r7c8, r8c8)
Eliminate 2 from r3c3 using the conjugate pairs (r6c6, r7c6) and (r7c8, r8c8)
Eliminate 2 from r8c2 using the xy-wing for (38) pivoted on r3c3 (pincers r3c2 and r3c7)
The 2 in box 7 occupies row 9; eliminate it from r9c4 and r9cS
Eliminate 2 from r6c4 using the xy-wing for (38) pivoted on r3c3 (pincers r3c7 and r6c6)
The only place for 2 in column 4 is rlc4

Steve

by **ravel** » Fri Mar 09, 2007 3:40 pm

Hi udosuk,

this is my first attempt for a harder X, so please verify.

Turbot fishes for 7: eliminate from r8c45, r9c4, r4c3
Gives r4c3=1, r9c9=1 and with pairs and locked candidates

Code: Select all: *--------------------------------------------------------------------* | 4 1 5 | 23 23 6 | 7 8 9 | | 9 6 23 | 78 78 4 | 23 1 5 | | 7 28 238 | 5 9 1 | 23 4 6 | |----------------------+----------------------+----------------------| | 8 4 1 | 37 6 37 | 5 9 2 | | 2 3 7 | 189 5 89 | 18 6 4 | | 5 9 6 | 248 1248 28 | 18 3 7 | |----------------------+----------------------+----------------------| | 13 5 248 | 6 12478 278 | 9 27 38 | | 13 278 2489 | 12489 1248 5 | 6 27 38 | | 6 278 289 | 2389 2378 23789 | 4 5 1 | *--------------------------------------------------------------------*

Again turbot fish eliminates 4 from r8c5, for 7 from r7c6 and 3 strong links 7 from r9c5. Pairs and locked candidates again:

Code: Select all: *--------------------------------------------------------------------* | 4 1 5 | 23 23 6 | 7 8 9 | | 9 6 23 | 78 78 4 | 23 1 5 | | 7 28 238 | 5 9 1 | 23 4 6 | |----------------------+----------------------+----------------------| | 8 4 1 | 37 6 37 | 5 9 2 | | 2 3 7 | 1 5 9 | 8 6 4 | | 5 9 6 | 248 248 28 | 1 3 7 | |----------------------+----------------------+----------------------| | 13 5 248 | 6 12478 28 | 9 27 38 | | 13 278 49 | 49 128 5 | 6 27 38 | | 6 278 289 | 2389 238 37 | 4 5 1 | *--------------------------------------------------------------------*

[/code]xyz-wing eliminates 2 from r78c5, gives pair 27 in r8c28.
Turbot fish eliminates 2 from r7c3, 3 strong links from r6c4.
UR 23 with 2 strong links in r19c45 eliminates 3 from r1c4.

Code: Select all: *--------------------------------------------------* | 4 1 5 | 2 3 6 | 7 8 9 | | 9 6 23 | 78 78 4 | 23 1 5 | | 7 28 238 | 5 9 1 | 23 4 6 | |----------------+----------------+----------------| | 8 4 1 | 37 6 37 | 5 9 2 | | 2 3 7 | 1 5 9 | 8 6 4 | | 5 9 6 | 48 248 28 | 1 3 7 | |----------------+----------------+----------------| | 1 5 48 | 6 47 28 | 9 27 3 | | 3 27 49 | 49 1 5 | 6 27 8 | | 6 278 289 | 39 28 37 | 4 5 1 | *--------------------------------------------------*

xyz-wing eliminates 2 from r9c3, the rest is singles.

by **udosuk** » Fri Mar 09, 2007 5:24 pm

Thanks tremendously for your work guys! Very impressive!

Steve R, very clever solution. However there are a few typos/mysterious symbols from your lines ("S"? "l"?) I took the priviledge to correct them myself (adding a simple box-line interaction), requoted as follows:

Steve R wrote:Eliminate 3 from r9c9 using the conjugate pairs (r3c3, r3c7) and (r4c4, r4c6)
The 3 in row 9 occupies box 8; eliminate it from r7c56 and r8c45
Eliminate 4 from r8c5 using the conjugate pairs (r6c4, r6c5) and (r7c3, r7c5)
Eliminate values using the pair (49) in row 8, columns 3 and 4
Eliminate 7 from r8c5 using the conjugate pairs (r2c4, r2c5) and (r4c4, r8c8)
Eliminate 7 from r9c4 using the conjugate pairs (r8c2, r9c2) and (r4c4, r8c8)
Eliminate 7 from r7c6 using the conjugate pairs (r4c6, r8c2) and (r7c8, r8c8)
Eliminate values using the pair (28) in column 6, rows 6 and 7
Eliminate 2 from r7c3 and r7c5 using the conjugate pairs (r6c6, r7c6) and (r7c8, r8c8)
Eliminate 2 from r3c3 using the conjugate pairs (r6c6, r7c6) and (r7c8, r8c8)
Eliminate 2 from r8c2 using the xy-wing for (38) pivoted on r3c3 (pincers r3c2 and r3c7)
The 2 in box 7 occupies row 9; eliminate it from r9c4 and r9c5
Eliminate 2 from r6c4 using the xy-wing for (38) pivoted on r3c3 (pincers r3c7 and r6c6)
The only place for 2 in column 4 is r1c4

ravel wrote:this is my first attempt for a harder X, so please verify.

I can follow your solution up until this line:

ravel wrote:Turbot fish eliminates 2 from r7c3, 3 strong links from r6c4.

I can see the turbot fish elimination r7c3<>2 using r7c6=2=r6c6=2=r8c8=2=r7c8

But I don't see how you could conclude r6c4<>2 using 3 strong links... As a matter of fact I tried putting r6c4=2 and solely from the pattern of 2s it is still possible, so you need to involve other candidates to conclude r6c4<>2... (Like the xy-wing shown by Steve R...)

But nonetheless thanks for the attempt!

Added later:

Based on the wisdom of Steve R, I think this is the shortest solution path:

Code: Select all: *--------------------------------------------------------------------------------------* | 4 1 5 | 23 23 6 | 7 8 9 | | 9 6 23 | 78 78 4 | 23 1 5 | | 7 28 238 | 5 9 1 | 23 4 6 | |----------------------------+----------------------------+----------------------------| | 8 4 17 | 137 6 37 | 5 9 2 | | 2 3 17 | 1789 5 789 | 18 6 4 | | 5 9 6 | 248 1248 28 | 18 3 7 | |----------------------------+----------------------------+----------------------------| | 13 5 248 | 6 123478 2378 | 9 27 138 | | 13 278 2489 | 1234789 123478 5 | 6 27 138 | | 6 278 289 | 123789 12378 23789 | 4 5 138 | *--------------------------------------------------------------------------------------*

Turbot fish on 7s: r4c6+r8c2 & r78c8 -> r7c6<>7
Generalised X-wing on 3s: r3c37 & r4c46 -> r9c9<>3
Locked candidates on 3s (r9,b8) -> r7c56+r8c45<>3
Naked pair {28} in r67c6 -> r5c6<>8, r9c6<>{28}
Generalised X-wing on 2s: r67c6 & r78c8 -> r3c3<>2, r7c35<>2
XY-wing on {238}: r3c3={38}, r3c7={23}, r3c2={28} -> r8c2<>2
XY-wing on {238}: r3c3={38}, r3c7={23}, r6c6={28} -> r6c4<>2

Hidden singles (d/) -> r3c7=2, r4c6=3, r8c2=7
Naked singles (d\) -> r8c8=2, r6c6=8, r3c3=3, r9c9=1, r4c4=7
Naked singles (d/) -> r6c4=4, r7c3=8

The rest are all naked singles.

by **ravel** » Fri Mar 09, 2007 6:34 pm

udosuk wrote:But I don't see how you could conclude r6c4<>2 using 3 strong links...

I neither

Dont know, what i have seen there.
Of course - xy-wings over the diagonal, didnt look for that.

by **udosuk** » Fri Mar 09, 2007 9:48 pm

Heck, after further studying no xy-wing or xyz-wing of any form is required... You just need a grouped turbot fish:

Code: Select all: 4 1 5 | 23 23 6 | 7 8 9 9 6 23 | 78 78 4 | 23 1 5 7 28 238 | 5 9 1 | 23 4 6 ---------------+-------------------------+------------- 8 4 17 | 137 6 37 | 5 9 2 2 3 17 | 1789 5 789 | 18 6 4 5 9 6 | 248 1248 28 | 18 3 7 ---------------+-------------------------+------------- 13 5 248 | 6 123478 2378 | 9 27 138 13 278 2489 | 1234789 123478 5 | 6 27 138 6 278 289 | 123789 12378 23789 | 4 5 138

Short version wrote:Generalised X-wing on 3s: r3c37 & r4c46 -> r9c9<>3
Locked candidates on 3s (n8,r9) -> r7c56+r8c45<>3
Generalised X-wing on 7s: r4c46 & r8c28 -> r4c3+r8c45<>7
Naked singles (n4) -> r45c3=[17]
Hidden single (d\) -> r9c9=1
Turbot fish on 7s: r4c6+r8c2 & r78c8 -> r7c6<>7
Naked pair {28} in r67c6 -> r5c6<>8, r9c6<>{28}
Grouped turbot fish on 8s: r3c3+r6c6 & r6c4+r7c3+r8c2 -> r89c3<>8
Turbot fish on 8s: r37c3 & r67c6 -> r7c59<>8
Naked singles (n9) -> r78c9=[38]
Generalised X-wing on 2s: r67c6 & r78c8 -> r3c3<>2, r7c35<>2
Pointing candidates on 2s: r3c27 -> r8c2<>2
Naked singles (d/) -> r8c2=7, r4c6=3, r3c7=2
The rest are all naked singles.

For fishing lovers, here is a longer version which catches a few more of unnecessary turbot fishes and x-wings

... No big fish (swordfish and above) though... I did mention in the Variant section that Sudoku X is a very productive environment for the turbot fish species...

Longer version wrote:Generalised X-wing on 3s: r3c37 & r4c46 -> r9c9<>3
Locked candidates on 3s (n8,r9) -> r7c56+r8c45<>3
Generalised X-wing on 7s: r4c46 & r8c28 -> r4c3+r8c45<>7
Naked singles (n4) -> r45c3=[17]
Hidden single (d\) -> r9c9=1
Turbot fish on 7s: r4c6+r8c2 & r78c8 -> r7c6<>7
Naked pair {28} in r67c6 -> r5c6<>8, r9c6<>{28}
Naked singles (n6) -> r5c6=9
Turbot fish on 7s: r4c4+r8c8 & r89c2 -> r9c4<>7
Turbot fish on 7s: r49c6 & r89c2 -> r9c5<>7
Turbot fish on 4s: r6c45 & r78c3 -> r8c5<>4
Hidden pair (r8) -> r8c34={49}
Hidden single (c4) -> r5c4=1
Naked singles (n6) -> r56c7=[81]
Grouped turbot fish on 8s: r3c3+r6c6 & r6c4+r7c3+r8c2 -> r9c3<>8
Turbot fish on 8s: r37c3 & r67c6 -> r7c59<>8
Naked singles (n9) -> r78c9=[38]
Naked singles (n7) -> r78c1=[13]
Hidden single (n8) -> r8c5=1
Turbot fish on 8s: r6c4+r7c3 & r67c6 -> r6c5<>8
Hidden pair (d/) -> r6c4+r7c3={48}
Generalised X-wing on 2s: r67c6 & r78c8 -> r3c3<>2, r7c5<>2
Pointing candidates on 2s: r3c27 -> r8c2<>2
The rest are all naked singles.