The New Sudoku Players' Forum

by **ncantoral** » Thu Jul 17, 2008 8:28 pm

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

only an x-wing and a xyz-wing, then brick wall

Code: Select all: --------------------------------------------------------- | 347 3478 247 | 5 39 6 | 124 189 129 | | 348 5 24 | 1 39 7 | 248 6 29 | | 1 9 6 | 2 4 8 | 3 7 5 | -------------------+------------------+------------------ | 9 46 145 | 7 256 3 | 1256 15 8 | | 356 36 8 | 4 256 1 | 7 359 2369 | | 2 367 157 | 8 56 9 | 156 13 4 | -------------------+------------------+------------------ | 78 2 3 | 6 178 5 | 9 4 17 | | 5678 1 9 | 3 78 4 | 568 2 67 | | 4567 4678 457 | 9 17 2 | 156 1358 1367 | ----------------------------------------------------------

by **daj95376** » Thu Jul 17, 2008 9:32 pm

There's a (78) UR in [r78c15] where I was able to perform [r8c1]<>8, but it doesn't help.
There's a (17) UR in [r79c59] where I was able to perform [r9c9]<>1, but it doesn't help.

The three chains that I found don't help, either.

However, there is a forcing net that leaves a Locked Naked Pair and then Singles.
(Let me know if my solver's notation is unacceptable.)

Code: Select all: 1r1c9 7r7c9 8r7c1 8r1c2 9r1c8 2r2c9 2r1c3 7r1c1 7r8c5 [b8]~ => [r1c9]<>1 c9b3 Locked Pair <> 29 [r1c78],[r2c7],[r5c9]

by **Steve K** » Thu Jul 17, 2008 10:39 pm

Not as quick, nor as elegant as daj's:
1) singles to 40 cells given or solved (up40)
2) (8)xwr19c28 => r1c17,r8c157<>8
3) (8)r9c8=(8-5)r8c7=(5)r8c1-(5)r5c1=(np36)r5c12-(3)r5c9=(3)r9c9 => r9c9<>3 => (3)r9c9
4) Wwing (8=7)r8c5-(7)r8c9=(7)r7c9-(7=8)r7c1 => r8c1,r7c5<>8 => some singles
5) (3)r56c2 => r5c1<>3
6) Wwing (5=6)r5c1-(6)r5c9=(6)r8c9-(6=5)r8c7 => r8c1<>5 => (5)r8c7
7) xy wing (6=5)r4c5-(5=1)r4c8-(1=6)r6c7 => r6c5<>6 => some singles
8) (hp45)r9c13 => (45)r9c13
9) (6)xw r58c19 => r5c2<>6 => some singles
10) BUG => (9)r1c9 singles to end

by **Carcul** » Mon Aug 11, 2008 8:12 am

Code: Select all: *----------------------------------------------------------* | 347 3478 247 | 5 39 6 | 124 189 129 | | 348 5 24 | 1 39 7 | 248 6 29 | | 1 9 6 | 2 4 8 | 3 7 5 | |-------------------+-------------------+------------------| | 9 46 145 | 7 256 3 | 1256 15 8 | | 356 36 8 | 4 256 1 | 7 359 2369 | | 2 367 157 | 8 56 9 | 156 135 4 | |-------------------+-------------------+------------------| | 78 2 3 | 6 178 5 | 9 4 17 | | 5678 1 9 | 3 78 4 | 568 2 67 | | 4567 4678 457 | 9 17 2 | 156 1358 1367 | *----------------------------------------------------------*

Let's suppose that r8c9=6. Then r8c1<>7, because of

=7=[r8c1](-7-[r127c1]-4-[r2c3]-2-[r2c9]-9-[r1c8])=3=[r9c9]=7=[r7c9]=
=1=[r1c9]-1-[(r1c8)]-8-[r9c8]=8=[r8c7]-8-[r8c5]-7-[r8c1].

But we also have [r9c9]=3|5=[r8c1]-5-[r5c12]-3-[r5c9]=3=[r9c9] which implies [r9c9]=3 and so =3=[r9c9]=7=[r7c9]=1=[r7c5]=8=[r8c5]=
=7=[r8c1], which is a contradiction. Therefore, r8c9<>6 and the puzzle is solved.