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123|456|789
457|189|236
698|327|154
-----------------
271|598|463
546|713|928
839|264|571
-----------------
364|972|815
785|641|392
912|835|647

... by: newby

(257)D1 using pairs 3D9E8; 8G7H8; 7G5H5 trying all combinations:
2D1; 3D9; 8G7; 7G5 solves

... by: JC Van Hay

In short : testing all the 16 combinations of 13 in Box 6 and 56 in Box 9 (with the help of 29H9, 29F4 and 8 in Box 9, if necessary) yield contradictions using "easy techniques"=(Loked Subsets + SingleDigitTechniques + UniquenessTests), except for DF9=31+G9.J7=56+2H9+8G7->solution.

In details :

a : E78 or E7D9 or F9E8 or F9D9=13
b : J87 or J8H9 or G9J7 or G9H9=56

a1 or b1 -> contradiction
a4 + b4 -> contradiction

a2b2->contradiction
a2b3+29H9->contradiction
a2b4->contradiction

a3b2->contradiction
a3b3+2H9+29F4->contradiction
a3b3+9H9+29F4+8G7H8->contradiction
a3b4->contradiction

a4b2->contradiction
a4b3+9H9->contradiction
a4b3+2H9+8H8->contradiction
a4b3+2H9+8G7->solution

... by: Sotir

UNSOLVED WEEKLY EXTREME # 82, SE=9.0
Original Grid:
9 . . | . . . | . 5 .
. 6 . | 4 . . | . . 9
8 . 5 | . 6 . | . . 3
------ +------ +------
. . . | 1 . . | 3 . 2
. . . | . . . | . . .
3 . 7 | . . 2 | . . .
------ +------ +------
4 . . | . 5 . | 7 . 6
7 . . | . . 8 | . 2 .
. 1 . | . . . | . . 5
SSTS
1) FXW(1):r3c87=r3c6-r7c6=r7c8,=>r2c8<>1
9 2347 1234 2378 12378 137 6 5 1478
12 6 123 4 12378 5 128 78 9
8 247 5 279 6 179 124 147 3
5 489 4689 1 4789 4679 3 46789 2
126 2489 124689 356789 34789 34679 4589 4789 478
3 489 7 5689 489 2 14589 14689 148
4 2389 2389 239 5 139 7 1389 6
7 5 369 369 1349 8 149 2 14
26 1 23689 23579 23479 34679 489 3489 5

2) (149=8)r89c97-(8=78)r2c785-(3)r2c5=r2c3-r1c2=r7c2-r7c8=(3)r9c8 ,=>r9c8<>49
3) Kraken,(1478)r1c9,=>r7c8<>3
a) (1)r1c9-r3c87=r3c6-r7c6=(1)r7c8
b) (4)r1c9-r3c87=(4-7)r3c2=(7-3)r1c2=(3)r7c2
c) (7)r1c9-(7=8)r2c8-(8=3)r9c8
d) (8)r1c9r2c87=(8-3)r2c5=r2c3-r1c2=(3)r7c2
4) (8)r7c8=r9c7-(8=78)r2c785-(3)r2c5=r2c3-r1c2=r7c2-r7c8=(3)r9c8 =>r7c2<>8
5)(1)r7c6=(1-8)r7c8=r9c7-(8=78)r2c785-(3)r2c5=r2c3-r1c2=r7c2-r7c8=(3)r9c8,=>r7c6<>3
6) AUR(12)r25c13:(2)r5c2=(3)r2c3-r1c2=(3)r7c2,=>r7c2<>2
7)(1)r5c3=r5c1-(1=2)r2c1-r13c2=(2)r5c2,=>r5c3<>2
8)Dynamic forcing chain,(2)r9c1,r79c3,=>r9c3<>69
a) (2)r9c1-(2=1)r2c1,=>-(1)r2c7
(2)r9c1-r5c1=r5c2,=>-(2)r3c2, (2)r9c1-r7c3=r7c4,=>-(2)r3c4,=>(2)r7c3,-(2)r2c7
-(12)r2c7,=>(8)r2c7-r9c7=(8)r9c3
b) (2-8)r7c3=(8)r9c3
c) (2)r9c3
9)(9)r9c456=(9-8)r9c7=(8-1)r7c8=(1)r7c6,=>r7c6<>9
10) (7=8)r2c8-r7c8=(8-2)r7c3=r7c4-(2=97)r3c46,=>r2c5<>7
11) (1=4)r3c8-(4=8)r1c9-(8=58)r156c4-(6)r6c4=(6)r6c8,=>r6c8<>1
12)(3=7)r1c6-(79=2)r3c46-r3c7=(2-8)r2c7=(8)r2c5,=>r2c5<>3
13)(8=2)r9c3-(2=12)r921c5-(8)r2c5=(8)r2c7,=>r9c7<>8
14)AUR(58)r56c47: (8)r1c4=(1)r6c7-(1=8)r6c9,=>r1c9<>8
15)YW: (7=2)r9c5-(2=9)r7c4-(9=7)r3c4,=>r9c4<>7.STE

.

... by: ray

Using only the basic strategies till run-out and then starting with cell J8{245} - bi-location for value 5 - and applying Fariadne's method(as per Puzzle #56).
Forcing J8 = 2 or 4 or 5 gives inconclusive result. Select D9{239} - bi-location for value 3 - to form a 2-cell tuple {J8,D9}. Forcing J8D9 = 22,23,42,43,53,59 gives inconclusive results while 29,52 gives contradictions. Select cell H2 - bi-location in value 8 - to form a 3-cell tuple {J8,D9,H2}.
Forcing J8D9H2 = 227,228,237,238,424,427,428 gives inconclusive results while 221,224,321,
234,421,431 gives contradictions. J8D8H2 = 438 gives a solution.
Using this solution, no 1-cell or 2-cell solutions were found. Many 3-clell solutions were found:
D1D9H8 = 239, E1E7H1 = 597, A8A9B9 = 896.