Passi risolutivi (40)
Passo 1
Hidden Singles
valore: 5.6
categoria doc: Getting_Started
4 in B4 is last in row/box
6 in A7 is last in column
6 in E4 is last in column/box
8 in G8 is last in row/box
Passo 2
Hidden Singles
valore: 4.9
categoria doc: Getting_Started
6 in C2 is last in row/box
6 in H8 is last in column/box
8 in C9 is last in row
Passo 3
Hidden Singles
valore: 4.5
categoria doc: Getting_Started
6 in D3 is last in row/column/box
6 in G1 is last in row/column/box
Passo 4
Naked Pair
valore: 21.9
categoria doc: Naked_Candidates
Naked Pair 1/3 on cells {F4|F8} means
- 1/3 can be removed from F2
- 1 can be removed from F7
Passo 5
Pointing Pairs
valore: 65.2
categoria doc: Intersection_Removal
Pair: between Box 9 and Col 9:
- 4 can be removed from E9
Passo 6
Naked Triple
valore: 85.8
categoria doc: Naked_Candidates
Naked Triple 4/5/8 on cells {E3|F2|F3} means
- 8 can be removed from E1
- 4 can be removed from E2
Passo 7
Hidden Singles
valore: 4.2
categoria doc: Getting_Started
8 in B1 is last in column
Passo 8
Rectangle Elimination
valore: 103.9
categoria doc: Rectangle_Elimination
If +2[H2] then -2[A2] forcing +2[A6] which removes all 2s from box 8, so H2 cannot be 2
Passo 9
Pointing Pairs
valore: 61.9
categoria doc: Intersection_Removal
Pair: between Box 7 and Col 3:
- 2 can be removed from B3
Passo 10
Aligned Pair Exclusion
valore: 570
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 1/5/7/9->1/7 and 1/2/5/9->1/2/5/9
- Combinations of 1/5/9 found in ALS {A1,A9}
- Combinations of 2/3/5/9 found in ALS {C4,C5,C6}
Passo 11
W-Wing
valore: 101.1
categoria doc: W_Wings
W-Wing (single). Either there is a 7 in A4 or in J8. They are connected through 1 in F4/F8, therefore
- 7 can be removed from J4
Passo 12
XY-Chain
valore: 259.3
categoria doc: XY_Chains
length=4, chain ends: A4 and B3
This proves 7 is the solution at one or possibly both ends of the chain
-7[A4]+1[A4]-1[A9]+9[A9]-9[A1]+5[A1]-5[B3]+7[B3]
- 7 can be removed from A2
- 7 can be removed from B5
Passo 13
Hidden Singles
valore: 4
categoria doc: Getting_Started
7 in A4 is last in row/box
Passo 14
Rectangle Elimination
valore: 97
categoria doc: Rectangle_Elimination
If +1[J6] then -1[A6] forcing +1[A9] which removes all 1s from box 9, so J6 cannot be 1
Passo 15
XY-Chain
valore: 327.4
categoria doc: XY_Chains
length=6, chain ends: F2 and G4
This proves 5 is the solution at one or possibly both ends of the chain
-5[F2]+4[F2]-4[F7]+8[F7]-8[D7]+1[D7]-1[F8]+3[F8]-3[F4]+1[F4]-1[G4]+5[G4]
- 5 can be removed from G2
Passo 16
Pointing Pairs
valore: 57.4
categoria doc: Intersection_Removal
Triple: between Box 7 and Row H:
- 5 can be removed from H6
Passo 17
WXYZ Wing
valore: 379.6
categoria doc: WXYZ_Wing
WXYZ Wing Type 1: The four cells {A9,A1,A2,B7} contain in total 1/2/5/9 with the hinge on A9.
Non-Restricted candidate 2 determines the 'wing' cells (in yellow) and one of those 2s must be true. Therefore...
- 2 can be removed from B2
Passo 18
Hidden Singles
valore: 3.7
categoria doc: Getting_Started
2 in A2 is last in column/box
Passo 19
WXYZ Wing
valore: 365.9
categoria doc: WXYZ_Wing
WXYZ Wing Type 1: The four cells {B7,A9,B5,B9} contain in total 1/2/3/9 with the hinge on B7.
Non-Restricted candidate 1 determines the 'wing' cells (in yellow) and one of those 1s must be true. Therefore...
- 1 can be removed from B8
Passo 20
Aligned Pair Exclusion
valore: 508.4
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 B8 / B9 reduced from 2/3/5/9->3/5/9 and 1/3/9->1/3/9
- Combinations of 1/2/9 found in ALS {A9,B7}
- Combinations of 5/7/9 found in ALS {B2,B3}
- Combinations of 1/2/3 found in ALS {B5,B7}
Note: some ALSs share cells and cannot be fully colour indicated
Passo 21
Grouped X-Cycle
valore: 396.4
categoria doc: Grouped_X_Cycles
X-CYCLE on 9 ((w.Groups) Discontinuous Alternating Nice Loop, length 6):
+9[C8]-9[B8|B9]+9[B2]-9[D2]+9[D8]-9[C8]
- Contradiction: When C8 is set to 9 the chain implies it cannot be 9 - it can be removed
Passo 22
Line/Unit Reduction
valore: 71.5
categoria doc: Intersection_Removal
Line/Box Reduction: 9s in box 2 remove the following in the same box:
- 9 can be removed from A6
Passo 23
Chute Remote Pair
valore: 88
categoria doc: Chute_Remote_Pairs
1 cannot be set in the yellow cells {D5,E5,F5} and with the Remote Pair in A6 and G4 it means:
- 5 can be removed from C4
- 5 can be removed from G6
Passo 24
Hidden Singles
valore: 3.5
categoria doc: Getting_Started
5 in G4 is last in row/column/box
Passo 25
Hidden Unique Rectangle
valore: 343.9
categoria doc: Hidden_Unique_Rectangles
Type 1: removing 3 at J6 because of CJ46 and two strong links on 9
Passo 26
Grouped X-Cycle
valore: 426.4
categoria doc: Grouped_X_Cycles
X-CYCLE on 1 ((w.Groups) Discontinuous Alternating Nice Loop, length 8):
+1[D6]-1[F4]+1[F8]-1[J8]+1[H9|J9]-1[A9]+1[A6]-1[D6]
- Contradiction: When D6 is set to 1 the chain implies it cannot be 1 - it can be removed
Passo 27
Y-Wing
valore: 135.4
categoria doc: Y_Wing_Strategy
Y-Wing pattern. Hinge: D6 (3/8), wings D7 F4, therefore
- 1 can be removed from F8
Last candidate 3 in F8 changed to solution
Passo 28
Naked Singles
valore: 1.6
categoria doc: Getting_Started
Last candidate 1 in F4 changed to solution
Passo 29
Hidden Singles
valore: 3.1
categoria doc: Getting_Started
3 in B9 is last in column/box
Passo 30
Naked Pair
valore: 14.7
categoria doc: Naked_Candidates
Naked Pair 3/8 on cells {D6|E6} means
- 3 can be removed from C6
- 3 can be removed from H6
Passo 31
X-Wing
valore: 86.7
categoria doc: X_Wing_Strategy
(Col->Row) 9 taken off E2, based on BD28
(Col->Row) 9 taken off E8, based on BD28
Passo 32
Chute Remote Pair
valore: 70.8
categoria doc: Chute_Remote_Pairs
1 cannot be set in the yellow cells {G7,H7,J7} and with the Remote Pair in A9 and D8 it means:
- 9 can be removed from B8
- 9 can be removed from E9
Last candidate 5 in B8 changed to solution
Passo 33
Naked Singles
valore: 1.4
categoria doc: Getting_Started
Last candidate 7 in B3 changed to solution
Last candidate 2 in C8 changed to solution
Passo 34
Naked Singles
valore: 1.2
categoria doc: Getting_Started
Last candidate 9 in B2 changed to solution
Last candidate 1 in B7 changed to solution
Last candidate 3 in C5 changed to solution
Passo 35
Naked Singles
valore: 1.1
categoria doc: Getting_Started
Last candidate 5 in A1 changed to solution
Last candidate 9 in A9 changed to solution
Last candidate 2 in B5 changed to solution
Last candidate 9 in C4 changed to solution
Last candidate 8 in D7 changed to solution
Passo 36
Naked Singles
valore: 0.9
categoria doc: Getting_Started
Last candidate 1 in A6 changed to solution
Last candidate 5 in C6 changed to solution
Last candidate 3 in D6 changed to solution
Last candidate 4 in F7 changed to solution
Last candidate 3 in J4 changed to solution
Passo 37
Naked Singles
valore: 0.7
categoria doc: Getting_Started
Last candidate 1 in D2 changed to solution
Last candidate 8 in E6 changed to solution
Last candidate 2 in E7 changed to solution
Last candidate 5 in F2 changed to solution
Last candidate 4 in G6 changed to solution
Last candidate 1 in J1 changed to solution
Passo 38
Naked Singles
valore: 0.5
categoria doc: Getting_Started
Last candidate 9 in D8 changed to solution
Last candidate 3 in E2 changed to solution
Last candidate 4 in E3 changed to solution
Last candidate 8 in F3 changed to solution
Last candidate 7 in G2 changed to solution
Last candidate 3 in H1 changed to solution
Last candidate 2 in H6 changed to solution
Last candidate 7 in J8 changed to solution
Passo 39
Naked Singles
valore: 0.2
categoria doc: Getting_Started
Last candidate 9 in E1 changed to solution
Last candidate 1 in E8 changed to solution
Last candidate 1 in G5 changed to solution
Last candidate 4 in H2 changed to solution
Last candidate 5 in H3 changed to solution
Last candidate 2 in J3 changed to solution
Last candidate 9 in J6 changed to solution
Last candidate 4 in J9 changed to solution
Passo 40
Naked Singles
valore: 0
categoria doc: Getting_Started
Last candidate 7 in E9 changed to solution
Last candidate 7 in H5 changed to solution
Last candidate 1 in H9 changed to solution