... by: Frans Goosens

#618

Combination 2-digits cells

C1=1 ( D1=5 ) Solved,

Total solving time is : 4 sec.
Number of logical steps is : 390

... by: Serban

@ Dieter
Sorry 1a. X-chain x=5 => [H1,FG2,G4,H7,D8] <>5
=> H1=7 OR F2=6 OR H7=4 OR F7=5 solve

... by: solve jo

@Dieter:

In the comment below, writing 'D9=7' is a typo, and 'D9<>7' is correct.

... by: solve jo

@Dieter:
D1=7 D9<>7, D8=7 D9<>7
These two solutions are weak links, which are necessary conditions to prove that D9=7, and are additionally connected chains to complement each other.

The Sudoku below is a section that gets blocked when executing the 'solve path' of the current site, and this technique was used to solve it.

Additionally, since proof is impossible with one AIC chain, you can only prove the correct answer by obtaining two more related AIC chains (they are only proof conditions, so no strong connection is required) and supplementing each chain.

This is a text version of the board useful for posting on forums:
+-------------------+---------------------+-------------------+
| 256 4 7 | 2358 2358 258 | 1 9 268 |
| 1256 3 158 | 12458 24578 9 | 4678 247 24678 |
| 12 128 9 | 1248 6 1278 | 478 3 5 |
+-------------------+---------------------+-------------------+
| 157 9 158 | 12568 258 4 | 3 257 2678 |
| 3 15678 1458 | 12568 258 12568 | 45678 2457 9 |
| 45 568 2 | 7 9 3 | 4568 1 468 |
+-------------------+---------------------+-------------------+
| 8 257 34 | 2356 1 2567 | 9 457 347 |
| 12457 1257 134 | 9 234578 2578 | 457 6 1347 |
| 9 157 6 | 345 3457 57 | 2 8 1347 |
+-------------------+---------------------+-------------------+

... by: Dieter

@solve jo:
D1=7 D9<>7 solve >> D1 cannot be 7, must be <> 7

... by: Dieter

@Serban:
1a. X-chain x=5 => [H1,FG2,G4,H7,D8] <>5 => G1=7 solve
G1 is preset by 8

... by: Dieter

#618 - basics: number 9 complete; F6=3
strategy: try to get hidden pairs or triplets
H1 = (1,2,4,5,7): 5 matrices
H1=7 solves

... by: solve jo

Forcing Net (Triple Forcing Chains) -> D9 delete 7

D1=7 D9<>7 solve

D8=7 D9<>7 solve

D9=7 (D1<>7 H1=7 H7<>7 G8=7 B8<>7) (D1<>7 H1=7 H1<>4 F1=4 E3<>4) (E8<>7 E2=7 E2<>6) D9<>6 D4=6 (E4<>6) E6<>6 E7=6 E7<>4 E8=4 B8<>4 B8=2 (A9<>2) B9<>2 D9=2 D9<>7 solve

... by: Serban

# 618 A8=C3=F5=G7=J1=9 F6=3 Basics to 28

1. Box 1 ABC123 n=4 e=5 Nc=1 Ns=1 => A1=2 basics to 54
1a. X-chain x=5 => [H1,FG2,G4,H7,D8] <>5 => G1=7 solve

2. Box 2 DEF123 n=3 e=6 Nc=1 Ns=1 => D1=5 solve

3. Box 9 GHJ789 n=4 e=5 Nc=20 Ns=20 => H7=4 & [G9=7 OR J9=3] solve