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by **ArkieTech** » Sun Jul 05, 2015 11:25 pm

Code: Select all: *-----------* |71.|..3|.2.| |5.8|4.7|...| |4..|...|...| |---+---+---| |1..|..9|..7| |..5|3.2|6..| |3..|8..|..2| |---+---+---| |...|...|..5| |...|2.4|1.8| |.4.|5..|.73| *-----------*

Play/Print this puzzle online

by **pjb** » Sun Jul 05, 2015 11:49 pm

Code: Select all: 7 1 6 | 9 58 3 | 58 2 4 5 29 8 | 4 26 7 | 39 139 169 4 239 239 | 1 2568 568 | 7 58 69 ------------------------+----------------------+--------------------- 1 28 24 | 6 45 9 | 3458 3458 7 89 7 5 | 3 a14 2 | 6 189-4 a19 3 6 49 | 8 7 b15 |b459 b1459 2 ------------------------+----------------------+--------------------- 2689 389 139 | 7 1689 168 | 249 469 5 69 5 7 | 2 3 4 | 1 69 8 2689 4 19 | 5 1689 168 | 29 7 3

(4=9)r5c59 - (9=4)r6c678 => -4 r5c8; stte

Phil

by **SteveG48** » Mon Jul 06, 2015 2:28 am

Code: Select all: *-----------------------------------------------------------* | 7 1 6 | 9 58 3 | 58 2 4 | | 5 b29 8 | 4 26 7 |b39 b139 b169 | | 4 239 239 | 1 2568 568 | 7 58 c69 | *-------------------+-------------------+-------------------| | 1 a28 24 | 6 45 9 | 3458 3458 7 | |a89 7 5 | 3 14 2 | 6 1489 1-9 | | 3 6 49 | 8 7 15 | 459 1459 2 | *-------------------+-------------------+-------------------| | 2689 389 139 | 7 1689 168 | 249 469 5 | | 69 5 7 | 2 3 4 | 1 69 8 | | 2689 4 19 | 5 1689 168 | 29 7 3 | *-----------------------------------------------------------*

(9=82)b4p24 - (2=1396)r2c2789 - (6=9)r3c9 => -9 r5c9 ; stte

by **Leren** » Mon Jul 06, 2015 3:07 am

Code: Select all: *--------------------------------------------------------------* | 7 1 6 | 9 58 3 | 58 2 4 | | 5 c29 8 | 4 26 7 | 39 139 169 | | 4 d239 d239 | 1 2568 568 | 7 58 e69 | |--------------------+--------------------+--------------------| | 1 b28 24 | 6 45 9 | 3458 3458 7 | |a89 7 5 | 3 14 2 | 6 1489 1-9 | | 3 6 49 | 8 7 15 | 459 1459 2 | |--------------------+--------------------+--------------------| | 2689 389 139 | 7 1689 168 | 249 469 5 | | 69 5 7 | 2 3 4 | 1 69 8 | | 2689 4 19 | 5 1689 168 | 29 7 3 | *--------------------------------------------------------------*

XY Wing with transport : (9=8) r5c1 - (8=2) r4c2 - (2=9) r2c2 - r3c23 = (9) r3c9 => - 9 r5c9; stte

Leren

by **Marty R.** » Mon Jul 06, 2015 4:50 am

Code: Select all: +--------------+------------+---------------+ | 7 1 6 | 9 58 3 | 58 2 4 | | 5 29 8 | 4 26 7 | 39 139 169 | | 4 239 239 | 1 2568 568 | 7 58 69 | +--------------+------------+---------------+ | 1 28 24 | 6 45 9 | 3458 3458 7 | | 89 7 5 | 3 14 2 | 6 1489 19 | | 3 6 49 | 8 7 15 | 459 1459 2 | +--------------+------------+---------------+ | 2689 389 139 | 7 1689 168 | 249 469 5 | | 69 5 7 | 2 3 4 | 1 69 8 | | 2689 4 19 | 5 1689 168 | 29 7 3 | +--------------+------------+---------------+

Play this puzzle online at the Daily Sudoku site

5r3c6=(5-1)r6c6=r6c8-(1=9)r5c9-(9=824)b4p234-(4=5)r4c5=>-5r13c5,r6c6

by **JC Van Hay** » Mon Jul 06, 2015 6:47 am

13 singles;

Code: Select all: +------------------+--------------+-------------------+ | 7 1 6 | 9 58 3 | 58 2 4 | | 5 239 8 | 4 26 7 | 39 1369 169 | | 4 239 239 | 1 2568 568 | 7 35689 69 | +------------------+--------------+-------------------+ | 1 28 2(4) | 6 5-4 9 | 3458 3458 7 | | 8(9) 7 5 | 3 (14) 2 | 6 1489 (19) | | 3 6 (49) | 8 7 15 | 459 1459 2 | +------------------+--------------+-------------------+ | 2689 2389 1239 | 7 1689 168 | 249 469 5 | | 69 5 7 | 2 3 4 | 1 69 8 | | 2689 4 129 | 5 1689 168 | 29 7 3 | +------------------+--------------+-------------------+

[(4=1)r5c5-(1=9)r5c9-9r5c1=(9-4)r6c3=4r4c3] - (4=5)r4c5; stte.

by **ArkieTech** » Mon Jul 06, 2015 1:47 pm

JC Van Hay wrote:13 singles;
Code: Select all
+------------------+--------------+-------------------+ | 7 1 6 | 9 58 3 | 58 2 4 | | 5 239 8 | 4 26 7 | 39 1369 169 | | 4 239 239 | 1 2568 568 | 7 35689 69 | +------------------+--------------+-------------------+ | 1 28 2(4) | 6 5-4 9 | 3458 3458 7 | | 8(9) 7 5 | 3 (14) 2 | 6 1489 (19) | | 3 6 (49) | 8 7 15 | 459 1459 2 | +------------------+--------------+-------------------+ | 2689 2389 1239 | 7 1689 168 | 249 469 5 | | 69 5 7 | 2 3 4 | 1 69 8 | | 2689 4 129 | 5 1689 168 | 29 7 3 | +------------------+--------------+-------------------+
[(4=1)r5c5-(1=9)r5c9-9r5c1=(9-4)r6c3=4r4c3] - (4=5)r4c5; stte.

I like the notation with no =>

by **Sudtyro2** » Mon Jul 06, 2015 3:53 pm

Code: Select all: *-----------------------------------------------------------* | 7 1 6 | 9 58 3 | 58 2 4 | | 5 29 8 | 4 26 7 | 39 139 69+1 | | 4 29+3 239 | 1 26+58 568 | 7 58 69 | *-------------------+-------------------+-------------------| | 1 28 24 | 6 5-4 9 | 3458 3458 7 | | 89 7 5 | 3 14 2 | 6 1489 19 | | 3 6 49 | 8 7 15 | 459 1459 2 | *-------------------+-------------------+-------------------| | 2689 389 139 | 7 1689 168 | 249 469 5 | | 69 5 7 | 2 3 4 | 1 69 8 | | 2689 4 19 | 5 1689 168 | 29 7 3 | *-----------------------------------------------------------*

Still learning about ADPs, so here's JC's elimination done the hard way...
ADP(269)r23c259 => -4r4c5; stte

First try using the internals (extra candidates) as noted in the above grid:

Code: Select all: 1r2c9 – (1=9)r5c9 – (9=284)b4p234 ---------------------4r4c5 || (5|8)r3c5 – (58=6)b2p29 – (6=91)r35c9 – (1=4)r5c5 -----4r4c5 || 3r3c2 - 3r3c3 || 2r3c3 – (2=4)r4c3 -----------------------------4r4c5 || 9r3c3 – r6c3 = r5c1 – (9=14)r5c59 -------------4r4c5

Now try using tlanglet's externals. Note that one can reuse some of the same chain segments present in the internals analysis.

For the DP 69s in b3, the 6s are locked, so use column external 9r5c9 to cover the 9s.

Code: Select all: 9r5c9 - (9=284)b4p234 ---------------------------------4r4c5

For the DP 26s in b2, the 2s are locked, so use box external 6r3c6 to cover the 6s.

Code: Select all: 6r3c6 - (6=91)r35c9 – (1=4)r5c5 -----------------------4r4c5

For the DP 29s in b1, use box externals (29)r3c3 to cover both the 2s and the 9s.

Code: Select all: 2r3c3 – (2=4)r4c3 -------------------------------------4r4c5 || 9r3c3 – r6c3 = r5c1 – (9=14)r5c59 ---------------------4r4c5

For this particular ADP, the externals analysis is perhaps a bit simpler than that for the internals. The user must ultimately decide which approach to take, and it may even be appropriate to use a mix of the two. Note that there are simpler ADPs in this grid, but the 3-candidate, 6-cell case above was a more interesting challenge.

And one additional comment is in order. Where appropriate I've used the “box/point” notation above when denoting multiple cells comprising mixed rows and columns within the same box. This convention is a definite space-saver and is easy to read and understand. See SteveG48's explanation in the June 21, 2015 Puzzle.

SteveC

by **Marty R.** » Mon Jul 06, 2015 5:50 pm

Steve, a couple of weeks ago I asked about the box-point thing that you use. I used it today. a few posts up. I think it's a great shortcut with no downside. Not just the time saved, but the clarity is vastly superior to the standard cell notation.

by **daj95376** » Mon Jul 06, 2015 8:53 pm

Hmmm! The marking of box positions is not new. It just wasn't accepted (put into practice) previously. Maybe it'll catch on now. There are several places where it can be used.

Code: Select all: +-----------------------+ | 7 1 . | . . 3 | . 2 . | | 5 . 8 | 4 . 7 | . . . | | 4 . . | . . . | . . . | |-------+-------+-------| | 1 . . | . . 9 | . . 7 | | . . 5 | 3 . 2 | 6 . . | | 3 . . | 8 . . | . . 2 | |-------+-------+-------| | . . . | . . . | . . 5 | | . . . | 2 . 4 | 1 . 8 | | . 4 . | 5 . . | . 7 3 | +-----------------------+ b3 Hidden Pair =58 b3p18 r2 b3 Locked Candidate 1 -3 r2c2 c8b9 Locked Candidate 1 -6 r2c8 c1b7 Locked Candidate 2 -2 b7p239 +--------------------------------------------------------------+ | 7 1 6 | 9 58 3 | 58 2 4 | | 5 29 8 | 4 26 7 | 39 139 169 | | 4 239 239 | 1 2568 568 | 7 58 69 | |--------------------+--------------------+--------------------| | 1 28 24 | 6 45 9 | 3458 3458 7 | | 89 7 5 | 3 14 2 | 6 1489 19 | | 3 6 49 | 8 7 15 | 459 1459 2 | |--------------------+--------------------+--------------------| | 2689 389 139 | 7 1689 168 | 249 469 5 | | 69 5 7 | 2 3 4 | 1 69 8 | | 2689 4 19 | 5 1689 168 | 29 7 3 | +--------------------------------------------------------------+ # 70 eliminations remain (4=9)r6c678 - (9=8)r5c589 - (8=5)r3c8 - r3c6 = r6c6 - (5=4)b6p678 => -4 b6p125

Is it now time to consider compressing bilocation SLs?

Code: Select all: (4=9)r6c678 - (9=8)r5c589 - (8=5)r3c8 -= 5r36c6 - (5=4)b6p678 => -4 b6p125 -also- (1=9)r5c9 -= 9b4p49 -= 4b4p93 -= 4b5p25 => -1 r5c5

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