Passi risolutivi (36)
Passo 1
Hidden Singles
valore: 5.6
categoria doc: Getting_Started
4 in H1 is last in row/box
7 in H6 is last in row
8 in D3 is last in row
8 in E4 is last in column/box
Passo 2
Hidden Singles
valore: 5
categoria doc: Getting_Started
5 in D5 is last in row
5 in F3 is last in box
7 in F4 is last in column/box
8 in G1 is last in column/box
Passo 3
Hidden Singles
valore: 4.6
categoria doc: Getting_Started
4 in B4 is last in column
Passo 4
Naked Pair
valore: 21.7
categoria doc: Naked_Candidates
Naked Pair 1/6 on cells {E1|E6} means
- 6 can be removed from E3
- 1/6 can be removed from E5
- 1/6 can be removed from E7
- 1/6 can be removed from E9
Last candidate 3 in E3 changed to solution
Last candidate 4 in E5 changed to solution
Passo 5
Hidden Singles
valore: 4
categoria doc: Getting_Started
4 in C9 is last in column
Passo 6
Pointing Pairs
valore: 59
categoria doc: Intersection_Removal
Pair: between Box 6 and Col 7:
- 6 can be removed from G7
- 6 can be removed from H7
Passo 7
XYZ Wing
valore: 234.4
categoria doc: XYZ_Wing
XYZ-Wing pattern. Hinge: G3 (2/6/9), wings G4 J1, therefore
- 6 can be removed from G2
Passo 8
Hidden Unique Rectangle
valore: 387.9
categoria doc: Hidden_Unique_Rectangles
Type 1: removing 1 at F2 because of DF28 and two strong links on 4
Passo 9
Simple Colouring
valore: 192.6
categoria doc: Singles_Chains
(RULE 4): Uncoloured candidate 1 in D7 can see two different coloured candidates of 1 elsewhere.
Last candidate 6 in D7 changed to solution
Passo 10
Hidden Unique Rectangle
valore: 374.1
categoria doc: Hidden_Unique_Rectangles
Type 2: removing 2 at B7 because of BE79 and one strong link on 7 between E9 and B9
Passo 11
WXYZ Wing
valore: 371.4
categoria doc: WXYZ_Wing
WXYZ Wing Type 1: The four cells {G5,F5,G2,G4} contain in total 1/2/3/6 with the hinge on G5.
Non-Restricted candidate 6 determines the 'wing' cells (in yellow) and one of those 6s must be true. Therefore...
- 6 can be removed from H5
Passo 12
Hidden Singles
valore: 3.7
categoria doc: Getting_Started
6 in H9 is last in row
Passo 13
Grouped X-Cycle
valore: 393.4
categoria doc: Grouped_X_Cycles
X-CYCLE on 3 ((w.Groups) Discontinuous Alternating Nice Loop, length 6):
+3[A7]-3[A6]+3[J6]-3[J9]+3[A9|B9]-3[A7]
- Contradiction: When A7 is set to 3 the chain implies it cannot be 3 - it can be removed
Passo 14
Grouped X-Cycle
valore: 390.4
categoria doc: Grouped_X_Cycles
X-CYCLE on 3 ((w.Groups) Discontinuous Alternating Nice Loop, length 6):
+3[A8]-3[A6]+3[J6]-3[J9]+3[A9|B9]-3[A8]
- Contradiction: When A8 is set to 3 the chain implies it cannot be 3 - it can be removed
Passo 15
Grouped X-Cycle
valore: 440.2
categoria doc: Grouped_X_Cycles
X-CYCLE on 6 ((w.Groups) Discontinuous Alternating Nice Loop, length 8):
+6[J6]-6[G4|J4]+6[A4]-6[C5|C6]+6[C3]-6[G3]+6[J1|J2|J3]-6[J6]
- Contradiction: When J6 is set to 6 the chain implies it cannot be 6 - it can be removed
Passo 16
Forcing Nets
valore: 244.6
categoria doc: Forcing_Nets
If C8 is not 2 then both candidates in E6 are ON so C8 must be 2
Depth: 7
len: 16
-2[C8]+9[C8]-9[C7]+9[G7]-1[G7]+1[G5]-1[F5]+1[E6]
-2[C8]+9[C8]-9[A8]+9[A1]-9[J1]+6[J1]-6[E1]+6[E6]
Last candidate 2 in C8 changed to solution
Passo 17
Forcing Nets
valore: 159.6
categoria doc: Forcing_Nets
If C5 is not 9 then candidates 1 in Row A are both ON so C5 must be 9
Depth: 5
len: 12
-9[C5]+9[B5]-2[B5]+2[A4]-2[A2]+1[A2]
-9[C5]+9[B5]-3[B5]+3[A6]-3[A9]+1[A9]
Last candidate 9 in C5 changed to solution
Passo 18
Naked Pair
valore: 15.1
categoria doc: Naked_Candidates
Naked Pair 2/3 on cells {B5|H5} means
- 2/3 can be removed from G5
Passo 19
Rectangle Elimination
valore: 75
categoria doc: Rectangle_Elimination
If +6[A1] then -6[E1] forcing +6[E6] which removes all 6s from Box 2, so A1 cannot be 6
Passo 20
Aligned Pair Exclusion
valore: 416
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 A4 / A6 reduced from 2/5/6->2/6 and 3/5/6->3/5/6
- Pair 2/3 found in ALS {B5}
- Pair 5/6 found in ALS {C6}
- Combinations of 1/3/5/8/9 found in ALS {A1,A7,A8,A9}
Passo 21
Hidden Singles
valore: 2.9
categoria doc: Getting_Started
5 in J4 is last in column
Passo 22
Pointing Pairs
valore: 42.5
categoria doc: Intersection_Removal
Pair: between Box 8 and Row G:
- 6 can be removed from G3
Passo 23
XY-Chain
valore: 182.4
categoria doc: XY_Chains
length=4, chain ends: G2 and J6
This proves 3 is the solution at one or possibly both ends of the chain
-3[G2]+2[G2]-2[G4]+6[G4]-6[G5]+1[G5]-1[J6]+3[J6]
- 3 can be removed from J2
Passo 24
Hidden Singles
valore: 2.8
categoria doc: Getting_Started
3 in G2 is last in column/box
Passo 25
XY-Chain
valore: 229.2
categoria doc: XY_Chains
length=6, chain ends: E7 and H5
This proves 2 is the solution at one or possibly both ends of the chain
-2[E7]+7[E7]-7[C7]+5[C7]-5[C6]+6[C6]-6[A4]+2[A4]-2[B5]+3[B5]-3[H5]+2[H5]
- 2 can be removed from H7
Passo 26
Hidden Singles
valore: 2.7
categoria doc: Getting_Started
2 in H5 is last in row
Passo 27
Naked Singles
valore: 1.2
categoria doc: Getting_Started
Last candidate 3 in B5 changed to solution
Last candidate 6 in G4 changed to solution
Passo 28
Naked Singles
valore: 1.1
categoria doc: Getting_Started
Last candidate 2 in A4 changed to solution
Last candidate 1 in G5 changed to solution
Passo 29
Naked Singles
valore: 1
categoria doc: Getting_Started
Last candidate 6 in F5 changed to solution
Last candidate 3 in J6 changed to solution
Passo 30
Naked Singles
valore: 1
categoria doc: Getting_Started
Last candidate 1 in E6 changed to solution
Last candidate 4 in F2 changed to solution
Passo 31
Naked Singles
valore: 0.9
categoria doc: Getting_Started
Last candidate 1 in D2 changed to solution
Last candidate 6 in E1 changed to solution
Passo 32
Naked Singles
valore: 0.7
categoria doc: Getting_Started
Last candidate 6 in A2 changed to solution
Last candidate 4 in D8 changed to solution
Last candidate 9 in J1 changed to solution
Passo 33
Naked Singles
valore: 0.5
categoria doc: Getting_Started
Last candidate 5 in A6 changed to solution
Last candidate 7 in C3 changed to solution
Last candidate 2 in G3 changed to solution
Last candidate 1 in J8 changed to solution
Passo 34
Naked Singles
valore: 0.2
categoria doc: Getting_Started
Last candidate 1 in A1 changed to solution
Last candidate 2 in B2 changed to solution
Last candidate 9 in B3 changed to solution
Last candidate 6 in C6 changed to solution
Last candidate 5 in C7 changed to solution
Last candidate 3 in F8 changed to solution
Last candidate 9 in G7 changed to solution
Last candidate 7 in J2 changed to solution
Last candidate 6 in J3 changed to solution
Last candidate 2 in J9 changed to solution
Passo 35
Naked Singles
valore: 0.1
categoria doc: Getting_Started
Last candidate 8 in A7 changed to solution
Last candidate 3 in A9 changed to solution
Last candidate 5 in B1 changed to solution
Last candidate 7 in E9 changed to solution
Last candidate 1 in F7 changed to solution
Last candidate 8 in H8 changed to solution
Passo 36
Naked Singles
valore: 0
categoria doc: Getting_Started
Last candidate 9 in A8 changed to solution
Last candidate 7 in B7 changed to solution
Last candidate 1 in B9 changed to solution
Last candidate 2 in E7 changed to solution
Last candidate 3 in H7 changed to solution