Passi risolutivi (39)
Passo 1
Hidden Singles
valore: 6.1
categoria doc: Getting_Started
2 in J7 is last in column/box
7 in A8 is last in column
7 in F7 is last in row/box
7 in H4 is last in column/box
Passo 2
Hidden Singles
valore: 5.7
categoria doc: Getting_Started
4 in C8 is last in column/box
Passo 3
Naked Pair
valore: 26.3
categoria doc: Naked_Candidates
Naked Pair 1/3 on cells {A7|A9} means
- 3 can be removed from A2
- 1/3 can be removed from A3
- 1/3 can be removed from A4
- 3 can be removed from A6
- 1/3 can be removed from B7
- 1/3 can be removed from C9
Passo 4
Hidden Pair
valore: 51.2
categoria doc: Hidden_Candidates
Hidden Pair 2/6 in Row D, on cells {D5|D6}
- removes 8/9 from D5
- removes 3/8/9 from D6
Passo 5
Hidden Singles
valore: 5
categoria doc: Getting_Started
9 in D8 is last in row
Passo 6
Hidden Pair
valore: 47.6
categoria doc: Hidden_Candidates
Hidden Pair 3/8 in Col 6, on cells {B6|E6}
- removes 4/9 from B6
- removes 4/9 from E6
Passo 7
Hidden Singles
valore: 4.7
categoria doc: Getting_Started
9 in E4 is last in row/box
Passo 8
Hidden Pair
valore: 44.3
categoria doc: Hidden_Candidates
Hidden Pair 6/9 in Box 9, on cells {G9|H9}
- removes 1/3/5 from G9
- removes 3/5/8 from H9
Passo 9
Pointing Pairs
valore: 66
categoria doc: Intersection_Removal
Pair: between Box 9 and Col 8:
- 1 can be removed from E8
Passo 10
Pointing Pairs
valore: 65.6
categoria doc: Intersection_Removal
Pair: between Box 5 and Row F:
- 4 can be removed from F3
Passo 11
Line/Unit Reduction
valore: 86.4
categoria doc: Intersection_Removal
Line/Box Reduction: 2s in box 2 remove the following in the same box:
- 2 can be removed from A6
- 2 can be removed from C5
Passo 12
Rectangle Elimination
valore: 107.3
categoria doc: Rectangle_Elimination
If +5[B3] then -5[F3] forcing +5[F9] which removes all 5s from Box 3, so B3 cannot be 5
Passo 13
Rectangle Elimination
valore: 106.6
categoria doc: Rectangle_Elimination
If +8[E9] then -8[C9] forcing +8[C5] which removes all 8s from Box 5, so E9 cannot be 8
Passo 14
Unique Rectangle 2+
valore: 210.5
categoria doc: Unique_Rectangles
Uniqueness Type 4 (Row) removing 6 from roof because of D5,D6,G5,G6
Passo 15
WXYZ Wing
valore: 418.2
categoria doc: WXYZ_Wing
WXYZ Wing Type 1: The four cells {B4,B6,C5,F4} contain in total 1/3/4/8 with the hinge on B4.
Non-Restricted candidate 3 determines the 'wing' cells (in yellow) and one of those 3s must be true. Therefore...
- 3 can be removed from C4
Passo 16
Pointing Pairs
valore: 61.5
categoria doc: Intersection_Removal
Pair: between Box 2 and Row B:
- 3 can be removed from B1
- 3 can be removed from B2
- 3 can be removed from B3
Passo 17
XY-Chain
valore: 305.4
categoria doc: XY_Chains
length=5, chain ends: B2 and F5
This proves 4 is the solution at one or possibly both ends of the chain
-4[B2]+5[B2]-5[B7]+8[B7]-8[B6]+3[B6]-3[E6]+8[E6]-8[F5]+4[F5]
- 4 can be removed from B5
Passo 18
Aligned Pair Exclusion
valore: 566.2
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 B4 / B5 reduced from 1/3/4->1/3/4 and 1/8/9->1/9
- Combinations of 4/5/8 found in ALS {B2,B7}
- Combinations of 1/3/8 found in ALS {B6,C5}
Passo 19
X-Wing
valore: 120.5
categoria doc: X_Wing_Strategy
(Row->Col) 8 taken off F3, based on CF59
Passo 20
Grouped X-Cycle
valore: 438.8
categoria doc: Grouped_X_Cycles
X-CYCLE Rule 3 ((w.Groups) Discontinuous Alternating Nice Loop, length 6):
+9[G3]-9[A3]+9[A6]-9[J6]+9[J1|J3]-9[G3]
- Contradiction: When G3 is set to 9 the chain implies it cannot be 9 - it can be removed
Passo 21
Grouped X-Cycle
valore: 435.8
categoria doc: Grouped_X_Cycles
X-CYCLE Rule 3 ((w.Groups) Discontinuous Alternating Nice Loop, length 6):
+9[H3]-9[A3]+9[A6]-9[J6]+9[J1|J3]-9[H3]
- Contradiction: When H3 is set to 9 the chain implies it cannot be 9 - it can be removed
Passo 22
Forcing Nets
valore: 156.3
categoria doc: Forcing_Nets
If A4 is not 6 then all 2s in Col 5 are removed so A4 must be 6
Depth: 4 len: 10
-6[A4]+6[A6]-6[D6]+6[D5]-2[D5]
-6[A4]+6[J4]-1[J4]+1[G5]-2[G5]
Last candidate 6 in A4 changed to solution
Passo 23
Hidden Singles
valore: 3.8
categoria doc: Getting_Started
2 in A2 is last in row
2 in C4 is last in column/box
Passo 24
Rectangle Elimination
valore: 91.5
categoria doc: Rectangle_Elimination
If +4[J6] then -4[A6] forcing +4[A3] which removes all 4s from Box 7, so J6 cannot be 4
Passo 25
Forcing Nets
valore: 145.3
categoria doc: Forcing_Nets
If B6 is not 8 then all 1s in Col 3 are removed so B6 must be 8
Depth: 4 len: 10
-8[B6]+8[C5]-1[C5]+1[C1]-1[B3]
-8[B6]+8[B7]-8[D7]+8[D3]-1[D3]
Last candidate 8 in B6 changed to solution
Passo 26
Naked Singles
valore: 1.5
categoria doc: Getting_Started
Last candidate 5 in B7 changed to solution
Last candidate 1 in C5 changed to solution
Last candidate 3 in E6 changed to solution
Passo 27
Naked Singles
valore: 1.3
categoria doc: Getting_Started
Last candidate 4 in B2 changed to solution
Last candidate 9 in B5 changed to solution
Last candidate 8 in C9 changed to solution
Last candidate 4 in F4 changed to solution
Passo 28
Naked Singles
valore: 1.1
categoria doc: Getting_Started
Last candidate 9 in A3 changed to solution
Last candidate 4 in A6 changed to solution
Last candidate 3 in B4 changed to solution
Last candidate 8 in F5 changed to solution
Last candidate 2 in G5 changed to solution
Last candidate 1 in J4 changed to solution
Passo 29
Naked Singles
valore: 1.1
categoria doc: Getting_Started
Last candidate 6 in D5 changed to solution
Passo 30
Naked Singles
valore: 1.1
categoria doc: Getting_Started
Last candidate 2 in D6 changed to solution
Last candidate 4 in H5 changed to solution
Passo 31
Hidden Singles
valore: 2
categoria doc: Getting_Started
1 in G8 is last in row/column/box
4 in E1 is last in row/box
4 in J3 is last in column
Passo 32
Hidden Singles
valore: 1.8
categoria doc: Getting_Started
1 in E9 is last in row
3 in H8 is last in column
Passo 33
Naked Singles
valore: 0.7
categoria doc: Getting_Started
Last candidate 3 in A9 changed to solution
Last candidate 8 in H7 changed to solution
Passo 34
Naked Singles
valore: 0.5
categoria doc: Getting_Started
Last candidate 1 in A7 changed to solution
Last candidate 3 in D7 changed to solution
Last candidate 5 in F9 changed to solution
Last candidate 5 in H3 changed to solution
Last candidate 5 in J8 changed to solution
Passo 35
Naked Singles
valore: 0.3
categoria doc: Getting_Started
Last candidate 1 in D1 changed to solution
Last candidate 8 in E8 changed to solution
Last candidate 3 in F3 changed to solution
Last candidate 9 in J1 changed to solution
Passo 36
Naked Singles
valore: 0.2
categoria doc: Getting_Started
Last candidate 7 in B1 changed to solution
Last candidate 8 in D3 changed to solution
Last candidate 5 in E2 changed to solution
Last candidate 7 in G3 changed to solution
Last candidate 6 in J6 changed to solution
Passo 37
Naked Singles
valore: 0.1
categoria doc: Getting_Started
Last candidate 1 in B3 changed to solution
Last candidate 3 in C2 changed to solution
Last candidate 3 in G1 changed to solution
Last candidate 9 in H6 changed to solution
Last candidate 8 in J2 changed to solution
Passo 38
Naked Singles
valore: 0
categoria doc: Getting_Started
Last candidate 5 in C1 changed to solution
Last candidate 6 in G2 changed to solution
Last candidate 5 in G6 changed to solution
Last candidate 6 in H9 changed to solution
Passo 39
Naked Singles
valore: 0
categoria doc: Getting_Started
Last candidate 9 in G9 changed to solution