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Monday 25-Jan-2021

... by: numpl_npm

This puzzle is SE11.8, but not so hard.

| _ 2 _ | 3 _ _ | _ _ _ | A
| 4 _ _ | _ 1 _ | _ _ _ | B
| _ _ 9 | _ _ 5 | 8 _ _ | C

| 1 _ _ | _ 2 _ | _ _ _ | D
| _ _ 5 | _ _ 9 | 7 _ _ | E
| _ 3 _ | 5 _ _ | _ 4 _ | F

| _ _ _ | _ 5 _ | 6 _ _ | G
| _ _ 6 | _ _ _ | _ 8 7 | H
| _ _ _ | _ _ 7 | _ _ 9 | J

Exocet: J3 H6 [1234]G89
Almost (+1) SK loop: C12.AB3.DF3.E12.E45.DF6.AB6.C45

So with basics only,

1J3 & 1H4 & (x)G3 & -(x)H6 where x in 234 -> all contra.
2J3 & 2H4 & (x)G3 & -(x)H6 where x in 134 -> all contra.
3J3 & 3H5 & (x)G3 & -(x)H6 where x in 14 -> all contra.
4J3 & 4G9 & 4D6 & (x)G3 & -(x)H6 where x in 123 -> all contra.

3J3 & 3H5 & 2G3 & -2H6 ->
 1A3 3C1 2B6 9A4
 7CF5=[7C5 578A1.B23|7F5 7C3 58A1.B2]=6C2
 -> contra.

1J3 & 1H4 & [78]G3 -> contra.
2J3 & 2H4 & [78]G3 -> contra.
3J3 & 3H5 & 7G3 -> contra.
3J3 & 3H5 & 8G3 -> solved
4J3 & [78]G3 -> contra.

Sunday 24-Jan-2021

... by: Marek

JE2 (1234) G89 H6 J3:
-8J3
double UR threat => 12 and 23 are impossible base pairs
-2G9

We can use the double UR threat for trial and error:

4C9 => 13 G89 H6 J3 C8 E9 => contradiction with AICs

4A9 => 13 G89 H6 J3 (1 xor 3)C89 (1 xor 3)E89
=> at most one 2 in CE89
=> 2E89 – C89 = C4 – AB6 = G6 – G13 = HJ1 – E1 = E89 –
=> -2 B4 G4 FG1 => contradiction with AICs

Therefore 4G9.

The puzzle is still not solvable by this solver. YZF_Sudoku solves it with a ridiculous number of nets. The exocet provides little help past this point.
However, there is a net which uses only 1234 to eliminate 1G8, but it seems difficult to generalise.
I think it requires diagonal alignments of 1s, 2s and 3s.
The 4s cannot be in the same tier/stack either and they must share a line (parallel to base) with each of the two digits which share their boxes (here 1 and 3 in boxes 2 and 4).
One of them has to see one of the base cells.
Then the digit sharing a line with the 4 in those 4 boxes cannot form a base pair with 4 (here boxes 1245, 14B15).
I hope I am not just overcomplicating something that is generally known.

Sunday 24-Jan-2021

... by: numpl_npm

| _ 2 _ | 3 _ _ | _ _ _ | A
| 4 _ _ | _ 1 _ | _ _ _ | B
| _ _ 9 | _ _ 5 | 8 _ _ | C

| 1 _ _ | _ 2 _ | _ _ _ | D
| _ _ 5 | _ _ 9 | 7 _ _ | E
| _ 3 _ | 5 _ _ | _ 4 _ | F

| _ _ _ | _ 5 _ | 6 _ _ | G
| _ _ 6 | _ _ _ | _ 8 7 | H
| _ _ _ | _ _ 7 | _ _ 9 | J

Exocet [1234]G89 J3 H6 i.e. (u where u 1234)G89 -> (u)J3.H6
| 1G89 -> 1AF7=[1A7 1C2 1J3|1F7 1E4 1H6]=1J3.H6
| 2G89 -> 2FB7=[2F7 2E1 2J3|2B7 2C4 2H6]=2J3.H6
| 3G89 -> 3BD7=[3B7 3C1 3J3|3D7 3E5 3H6]=3J3.H6
| 4G9 -> 4A7 4BD6=[4B6 4E2 4J3|4D6]=4J3.H6

L1: 1J3 & 1H4
L2: 2J3 & 2H4
L3: 3J3 & 3H5
L4: 4J3 & 4H45

R1: 1J2 & 1H6 & [234]J3
R2: 2J1 & 2H6 & [134]J3
R3: 3J1 & 3H6 & [124]J3
R4: 4J2 & 4H6 & [123]J3

With DFC(Digit Forcing Chains),

24AB6 -> contra.

24E12 -> contra.

13AB3 -> contra.

13C12 -> contra.
| 24AB6 -> contra.
| 2[68]AB6 -> contra.
| 4[68]AB6 -> contra.

68AB6 -> contra.
| 3D6 -> contra.
| 4D6 -> contra.

R1 -> ... -2G89 -2J3 ... 1A3 3C1 ... contra.
R2 -> ... -3G89 -3J3 ... 3B3 1C2 ... contra.

L1 -> -2G89(∵R2 contra.) -4G89(∵R2 -1G8) 3J1 3H6 ... contra.
L3 -> -12G89(∵R1 and R2 contra.) 4J2 4H6 4G9 3G8 ... solved
L4 -> -12G89(∵R1 and R2 contra.) 3J1 3H6 3G8 4G9 ... contra.

L2 x R3 -> 23G89 ... contra.
L2 x R4 -> 24G89 ... contra.

Saturday 23-Jan-2021

... by: Frans Goosens

With trial and error

Combination C2=167 and F6=168

************************************************************
C2=1 F6=1 No solution, Fixed

Combination 2-digits cells

A3=7 No solution, Undo calculation
A3=8 No solution, Undo calculation
F7=2 No solution, Undo calculation
F7=9 No solution, Undo calculation

All reset to initial position

************************************************************
C2=1 F6=6 No solution, Fixed

Combination 2-digits cells

A3=7 Wrong, Undo calculation
A3=8 Wrong, Undo calculation

All reset to initial position

************************************************************
C2=1 F6=8 No solution, Fixed

Combination 2-digits cells

A3=7 Wrong, Undo calculation
A3=8 Wrong, Undo calculation

All reset to initial position

************************************************************
C2=6 F6=1 No solution, Fixed

Combination 2-digits cells

C1=3 No solution, Undo calculation
C1=7 Wrong, Undo calculation
C1=3 No solution, Fixed
B3=7 Wrong, Undo calculation
B3=8 Wrong, Undo calculation

All reset to initial position

************************************************************
C2=6 F6=6 Wrong, Undo calculation

All reset to initial position

************************************************************
C2=6 F6=8 ( A6=6 ) Solved,


#436--------------------------Solution
020 300 000-------------821 396 475
400 010 000-------------457 812 396
009 005 800-------------369 475 812

100 020 000-------------194 723 568
005 009 700-------------685 149 723
030 500 040-------------732 568 941

000 050 600-------------978 251 634
006 000 087-------------516 934 287
000 007 009-------------243 687 159

Total solving time is : 260 sec.
Number of logical steps is : 23577

Saturday 23-Jan-2021

... by: James Havard

Tough one. 39 subs and 61 seconds to get 5 subs for the bottom box row and could only reduce to 3 subs to get a singles solution. G4=2 G6=1 J7=1

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