Passi risolutivi (41)
Passo 1
Naked Singles
valore: 1
categoria doc: Getting_Started
Last candidate 3 in J7 changed to solution
Passo 2
Hidden Singles
valore: 5.4
categoria doc: Getting_Started
3 in A9 is last in row
6 in C2 is last in row/box
6 in E3 is last in column
6 in J8 is last in row
7 in E6 is last in column/box
Passo 3
Hidden Singles
valore: 4.7
categoria doc: Getting_Started
6 in F5 is last in row/box
6 in G4 is last in column
7 in F2 is last in column/box
8 in A4 is last in row
Passo 4
Hidden Singles
valore: 4.1
categoria doc: Getting_Started
7 in C7 is last in column
8 in H5 is last in row/column/box
Passo 5
Naked Pair
valore: 19.1
categoria doc: Naked_Candidates
Naked Pair 2/9 on cells {A2|B2} means
- 2 can be removed from B3
- 2/9 can be removed from C1
- 2 can be removed from E2
- 2/9 can be removed from G2
- 2 can be removed from H2
Passo 6
Hidden Singles
valore: 3.7
categoria doc: Getting_Started
2 in G3 is last in column
2 in H4 is last in row
Passo 7
Line/Unit Reduction
valore: 69.3
categoria doc: Intersection_Removal
Line/Box Reduction: 1s in box 6 remove the following in the same box:
- 1 can be removed from D8
- 1 can be removed from D9
- 1 can be removed from E8
- 1 can be removed from E9
Passo 8
Y-Wing
valore: 137.6
categoria doc: Y_Wing_Strategy
Y-Wing pattern. Hinge: C1 (5/8), wings C9 D1, therefore
- 4 can be removed from D9
Passo 9
Simple Colouring
valore: 170.6
categoria doc: Singles_Chains
(RULE 4): Uncoloured candidate 1 in G5 can see two different coloured candidates of 1 elsewhere.
Passo 10
Pointing Pairs
valore: 50.8
categoria doc: Intersection_Removal
Triple: between Box 8 and Col 6:
- 1 can be removed from C6
Passo 11
X-Cycle
valore: 251.7
categoria doc: X_Cycles
X-CYCLE on 9 (Discontinuous Alternating Nice Loop, length 8):
+9[B5]-9[B2]+9[A2]-9[A7]+9[E7]-9[D8]+9[D5]-9[B5]
- Contradiction: When B5 is set to 9 the chain implies it cannot be 9 - it can be removed
Passo 12
XY-Chain
valore: 214.6
categoria doc: XY_Chains
length=4, chain ends: B4 and J6
This proves 9 is the solution at one or possibly both ends of the chain
-9[B4]+5[B4]-5[B3]+8[B3]-8[J3]+1[J3]-1[J6]+9[J6]
- 9 can be removed from B6
- 9 can be removed from C6
Passo 13
Line/Unit Reduction
valore: 65.5
categoria doc: Intersection_Removal
Line/Box Reduction: 9s in box 8 remove the following in the same box:
- 9 can be removed from G5
Passo 14
Naked Triple
valore: 63.3
categoria doc: Naked_Candidates
Naked Triple 4/5/8 on cells {C1|C6|C9} means
- 5 can be removed from C4
- 5 can be removed from C5
- 4/8 can be removed from C8
Passo 15
Naked Pair
valore: 15.5
categoria doc: Naked_Candidates
Naked Pair 2/9 on cells {A7|C8} means
- 2/9 can be removed from B8
Passo 16
Rectangle Elimination
valore: 77
categoria doc: Rectangle_Elimination
If +5[E1] then -5[E4] forcing +5[B4] which removes all 5s from Box 1, so E1 cannot be 5
Passo 17
X-Cycle
valore: 183.2
categoria doc: X_Cycles
X-CYCLE on 5 (Discontinuous Alternating Nice Loop, length 6):
+5[D5]-5[E4]+5[B4]-5[B3]+5[D3]-5[D5]
- Contradiction: When D5 is set to 5 the chain implies it cannot be 5 - it can be removed
Passo 18
Pointing Pairs
valore: 45
categoria doc: Intersection_Removal
Pair: between Box 5 and Row E:
- 5 can be removed from E7
- 5 can be removed from E9
Passo 19
Naked Pair
valore: 14.9
categoria doc: Naked_Candidates
Naked Pair 4/8 on cells {C9|E9} means
- 4 can be removed from G9
Passo 20
XY-Chain
valore: 279.6
categoria doc: XY_Chains
length=7, chain ends: C1 and F7
This proves 5 is the solution at one or possibly both ends of the chain
-5[C1]+8[C1]-8[B3]+5[B3]-5[B4]+9[B4]-9[B2]+2[B2]-2[A2]+9[A2]-9[A7]+2[A7]-2[F7]+5[F7]
- 5 can be removed from F1
Passo 21
Pointing Pairs
valore: 43.7
categoria doc: Intersection_Removal
Pair: between Box 4 and Row D:
- 5 can be removed from D9
Last candidate 7 in D9 changed to solution
Passo 22
Hidden Singles
valore: 2.8
categoria doc: Getting_Started
7 in G8 is last in row/column/box
Passo 23
Pointing Pairs
valore: 40.9
categoria doc: Intersection_Removal
Pair: between Box 9 and Row H:
- 4 can be removed from H2
Passo 24
XY-Chain
valore: 175.2
categoria doc: XY_Chains
length=4, chain ends: H8 and J6
This proves 1 is the solution at one or possibly both ends of the chain
-1[H8]+4[H8]-4[B8]+8[B8]-8[B3]+8[J3]-1[J3]+1[J6]
- 1 can be removed from H6
Passo 25
Naked Pair
valore: 13.2
categoria doc: Naked_Candidates
Naked Pair 3/5 on cells {G5|H6} means
- 3/5 can be removed from G6
Passo 26
XY-Chain
valore: 196
categoria doc: XY_Chains
length=5, chain ends: F1 and G5
This proves 3 is the solution at one or possibly both ends of the chain
-3[F1]+2[F1]-2[F7]+5[F7]-5[F9]+1[F9]-1[G9]+5[G9]-5[G5]+3[G5]
- 3 can be removed from G1
Passo 27
Hidden Pair
valore: 25.9
categoria doc: Hidden_Candidates
Hidden Pair 2/3 in Col 1, on cells {E1|F1}
- removes 4 from E1
Passo 28
Naked Pair
valore: 12.8
categoria doc: Naked_Candidates
Naked Pair 2/3 on cells {E1|F1} means
- 3 can be removed from E2
Passo 29
XY-Chain
valore: 212.8
categoria doc: XY_Chains
length=6. This XY-Chain is continuous and one value in each cell must be the solution, so all off-chain candidates can be removed
-4[E9]+8[E9]-8[C9]+4[C9]-4[B8]+8[B8]-8[B3]+8[C1]-5[C1]+5[D1]-4[D1]+4[E2]
- 4 can be removed from E7
- 4 can be removed from E8
Passo 30
Hidden Singles
valore: 2.5
categoria doc: Getting_Started
4 in H7 is last in column
Passo 31
Naked Singles
valore: 1.2
categoria doc: Getting_Started
Last candidate 1 in H8 changed to solution
Passo 32
Naked Singles
valore: 1.1
categoria doc: Getting_Started
Last candidate 5 in G9 changed to solution
Last candidate 3 in H2 changed to solution
Passo 33
Naked Singles
valore: 1
categoria doc: Getting_Started
Last candidate 1 in F9 changed to solution
Last candidate 3 in G5 changed to solution
Last candidate 5 in H6 changed to solution
Passo 34
Naked Singles
valore: 0.9
categoria doc: Getting_Started
Last candidate 4 in C6 changed to solution
Passo 35
Naked Singles
valore: 0.9
categoria doc: Getting_Started
Last candidate 3 in B6 changed to solution
Last candidate 8 in C9 changed to solution
Passo 36
Naked Singles
valore: 0.8
categoria doc: Getting_Started
Last candidate 4 in B8 changed to solution
Last candidate 5 in C1 changed to solution
Last candidate 4 in E9 changed to solution
Passo 37
Naked Singles
valore: 0.6
categoria doc: Getting_Started
Last candidate 8 in B3 changed to solution
Last candidate 4 in D1 changed to solution
Last candidate 9 in D8 changed to solution
Last candidate 1 in E2 changed to solution
Passo 38
Naked Singles
valore: 0.4
categoria doc: Getting_Started
Last candidate 2 in C8 changed to solution
Last candidate 5 in D3 changed to solution
Last candidate 1 in D5 changed to solution
Last candidate 2 in E7 changed to solution
Last candidate 9 in G1 changed to solution
Last candidate 4 in G2 changed to solution
Last candidate 1 in J3 changed to solution
Passo 39
Naked Singles
valore: 0.2
categoria doc: Getting_Started
Last candidate 9 in A7 changed to solution
Last candidate 9 in C5 changed to solution
Last candidate 3 in E1 changed to solution
Last candidate 5 in F7 changed to solution
Last candidate 3 in F8 changed to solution
Last candidate 1 in G6 changed to solution
Last candidate 8 in J1 changed to solution
Last candidate 9 in J6 changed to solution
Passo 40
Naked Singles
valore: 0
categoria doc: Getting_Started
Last candidate 2 in A2 changed to solution
Last candidate 5 in B4 changed to solution
Last candidate 1 in C4 changed to solution
Last candidate 5 in E5 changed to solution
Last candidate 8 in E8 changed to solution
Last candidate 2 in F1 changed to solution
Passo 41
Naked Singles
valore: 0
categoria doc: Getting_Started
Last candidate 9 in B2 changed to solution
Last candidate 2 in B5 changed to solution
Last candidate 9 in E4 changed to solution