Passi risolutivi (29)
Passo 1
Naked Singles
valore: 0
categoria doc: Getting_Started
Last candidate 5 in E4 changed to solution
Last candidate 1 in E6 changed to solution
Passo 2
Hidden Singles
valore: 5.1
categoria doc: Getting_Started
1 in A3 is last in row/column/box
1 in D8 is last in row/box
1 in H9 is last in column
2 in B1 is last in column/box
5 in F2 is last in row/box
Passo 3
Hidden Singles
valore: 4.6
categoria doc: Getting_Started
1 in G5 is last in row/column/box
5 in A1 is last in column/box
Passo 4
Naked Pair
valore: 21.3
categoria doc: Naked_Candidates
Naked Pair 2/9 on cells {D5|F5} means
- 9 can be removed from A5
- 9 can be removed from B5
- 2/9 can be removed from C5
- 9 can be removed from H5
- 2/9 can be removed from J5
Passo 5
Hidden Pair
valore: 41.5
categoria doc: Hidden_Candidates
Hidden Pair 4/8 in Row A, on cells {A2|A5}
- removes 3/6/9 from A2
- removes 3 from A5
Passo 6
Pointing Pairs
valore: 61.5
categoria doc: Intersection_Removal
Pair: between Box 7 and Col 3:
- 3 can be removed from B3
- 3 can be removed from C3
Passo 7
Pointing Pairs
valore: 61.1
categoria doc: Intersection_Removal
Pair: between Box 1 and Row C:
- 6 can be removed from C8
Passo 8
Pointing Pairs
valore: 60.2
categoria doc: Intersection_Removal
Pair: between Box 2 and Row A:
- 7 can be removed from A7
- 7 can be removed from A9
Passo 9
Rectangle Elimination
valore: 99.7
categoria doc: Rectangle_Elimination
If +5[J7] then -5[B7] forcing +5[B5] which removes all 5s from box 8, so J7 cannot be 5
Passo 10
Aligned Pair Exclusion
valore: 554.6
categoria doc: Aligned_Pair_Exclusion
Some solution combinations in the two gray cells would empty at least one of the coloured cells. Removing those combinations create eliminations in the gray cells.
Pair D7 / F7 reduced from 2/6/7->2/6/7 and 2/3/7/8->2/3/8
- Pair 6/8 found in ALS {E8}
- Pair 2/7 found in ALS {F9}
- Combinations of 3/5/6/7 found in ALS {A7,B7,H7}
Passo 11
Grouped X-Cycle
valore: 432.7
categoria doc: Grouped_X_Cycles
X-CYCLE on 6 ((w.Groups) Discontinuous Alternating Nice Loop, length 6):
+6[H8]-6[E8]+6[E2]-6[G2]+6[G7|G8]-6[H8]
- Contradiction: When H8 is set to 6 the chain implies it cannot be 6 - it can be removed
Passo 12
Grouped X-Cycle
valore: 429.7
categoria doc: Grouped_X_Cycles
X-CYCLE on 6 ((w.Groups) Discontinuous Alternating Nice Loop, length 6):
+6[J8]-6[E8]+6[E2]-6[G2]+6[G7|G8]-6[J8]
- Contradiction: When J8 is set to 6 the chain implies it cannot be 6 - it can be removed
Passo 13
Forcing Nets
valore: 310.3
categoria doc: Forcing_Nets
If A5 is not 8 then all 3s in Box 6 are removed so A5 must be 8
Depth: 8
len: 18
-8[A5]+8[A2]-8[E2]+8[E8]-6[E8]+6[D7]-6[A7]+3[A7]-3[F7]
-8[A5]+8[A2]-8[E2]+8[E8]-6[E8]+6[D7]-7[D7]+7[F8]-3[F8]
Last candidate 8 in A5 changed to solution
Passo 14
Naked Singles
valore: 1.8
categoria doc: Getting_Started
Last candidate 4 in A2 changed to solution
Passo 15
Hidden Singles
valore: 3.5
categoria doc: Getting_Started
4 in C5 is last in row/column/box
4 in G7 is last in row
Passo 16
Pointing Pairs
valore: 50.8
categoria doc: Intersection_Removal
Pair: between Box 9 and Row J:
- 2 can be removed from J4
- 2 can be removed from J6
Passo 17
X-Wing
valore: 99.9
categoria doc: X_Wing_Strategy
(Col->Row) 6 taken off C2, based on EG28
(Col->Row) 6 taken off D2, based on EG28
Passo 18
Hidden Singles
valore: 3.3
categoria doc: Getting_Started
6 in C3 is last in row/box
Passo 19
XYZ Wing
valore: 189.8
categoria doc: XYZ_Wing
XYZ-Wing pattern. Hinge: F3 (7/8/9), wings B3 D2, therefore
- 9 can be removed from D3
Passo 20
Forcing Nets
valore: 219.5
categoria doc: Forcing_Nets
If A7 is not 3 then candidates 7 in Row D are both ON so A7 must be 3
Depth: 7
len: 16
-3[A7]+6[A7]-6[A9]+6[J9]-6[J1]+6[G2]-7[G2]+7[D2]
-3[A7]+3[A4]-3[B5]+5[B5]-5[B7]+5[H7]-7[H7]+7[D7]
Last candidate 3 in A7 changed to solution
Passo 21
Hidden Singles
valore: 2.9
categoria doc: Getting_Started
3 in F8 is last in row/column/box
6 in A9 is last in row/box
Passo 22
Naked Pair
valore: 13.9
categoria doc: Naked_Candidates
Naked Pair 7/9 on cells {A4|A6} means
- 9 can be removed from C4
- 9 can be removed from C6
Passo 23
Line/Unit Reduction
valore: 53.9
categoria doc: Intersection_Removal
Line/Box Reduction: 7s in box 9 remove the following in the same box:
- 7 can be removed from H7
- 7 can be removed from J7
- 7 can be removed from J9
Passo 24
XY-Chain
valore: 280.2
categoria doc: XY_Chains
length=8, chain ends: B3 and F7
This proves 8 is the solution at one or possibly both ends of the chain
-8[B3]+9[B3]-9[C2]+3[C2]-3[C4]+2[C4]-2[C6]+5[C6]-5[C8]+9[C8]-9[B9]+7[B9]-7[F9]+2[F9]-2[F7]+8[F7]
- 8 can be removed from F3
Passo 25
Hidden Singles
valore: 2.6
categoria doc: Getting_Started
8 in B3 is last in column
8 in E2 is last in box
8 in F7 is last in row
Passo 26
Hidden Singles
valore: 2.1
categoria doc: Getting_Started
6 in D1 is last in row/box
6 in G2 is last in row/column
8 in J8 is last in row/column/box
Passo 27
Hidden Singles
valore: 1.7
categoria doc: Getting_Started
4 in D3 is last in row/column/box
7 in D2 is last in column
9 in F3 is last in column
Passo 28
Naked Singles
valore: 0.5
categoria doc: Getting_Started
Last candidate 9 in B9 changed to solution
Last candidate 5 in C8 changed to solution
Last candidate 9 in D5 changed to solution
Last candidate 5 in H7 changed to solution
Last candidate 7 in H8 changed to solution
Last candidate 2 in J9 changed to solution
Last candidate 3 in B2 changed to solution
Last candidate 5 in B5 changed to solution
Last candidate 7 in B7 changed to solution
Last candidate 9 in C2 changed to solution
Last candidate 2 in C6 changed to solution
Last candidate 9 in G8 changed to solution
Last candidate 3 in H3 changed to solution
Last candidate 6 in H5 changed to solution
Last candidate 7 in J3 changed to solution
Last candidate 3 in J5 changed to solution
Passo 29
Naked Singles
valore: 0
categoria doc: Getting_Started
Last candidate 3 in C4 changed to solution
Last candidate 7 in G6 changed to solution
Last candidate 9 in J4 changed to solution
Last candidate 5 in J6 changed to solution
Last candidate 7 in A4 changed to solution
Last candidate 9 in A6 changed to solution
Last candidate 2 in G4 changed to solution