Passi risolutivi (36)
Passo 1
Hidden Singles
valore: 5.6
categoria doc: Getting_Started
2 in A4 is last in row/box
3 in J1 is last in row/box
6 in J5 is last in row/box
8 in D6 is last in row/box
8 in G9 is last in column/box
Passo 2
Naked Singles
valore: 1
categoria doc: Getting_Started
Last candidate 7 in E5 changed to solution
Passo 3
Naked Singles
valore: 2.4
categoria doc: Getting_Started
Last candidate 9 in G5 changed to solution
Passo 4
Hidden Singles
valore: 4.5
categoria doc: Getting_Started
2 in G6 is last in row
4 in H4 is last in box
9 in B6 is last in column/box
Passo 5
Hidden Singles
valore: 4.1
categoria doc: Getting_Started
1 in B4 is last in box
1 in H6 is last in column
Passo 6
Hidden Singles
valore: 3.9
categoria doc: Getting_Started
1 in G8 is last in row/box
Passo 7
Naked Pair
valore: 18.6
categoria doc: Naked_Candidates
Naked Pair 3/7 on cells {C4|C6} means
- 7 can be removed from C1
- 7 can be removed from C2
- 3/7 can be removed from C9
Passo 8
Naked Pair
valore: 18
categoria doc: Naked_Candidates
Naked Pair 2/7 on cells {H3|H7} means
- 7 can be removed from H1
- 2/7 can be removed from H2
- 7 can be removed from H8
Passo 9
Pointing Pairs
valore: 53.6
categoria doc: Intersection_Removal
Pair: between Box 6 and Col 9:
- 2 can be removed from J9
Passo 10
Pointing Pairs
valore: 53.2
categoria doc: Intersection_Removal
Pair: between Box 3 and Row B:
- 6 can be removed from B2
Passo 11
Hidden Triple
valore: 87.3
categoria doc: Hidden_Candidates
Hidden Triple 5/6/8 in Box 1, on cells {B2|C1|C2}
- removes 7 from B2
- removes 4 from C1
Passo 12
XY-Chain
valore: 316.2
categoria doc: XY_Chains
length=7. This XY-Chain is continuous and one value in each cell must be the solution, so all off-chain candidates can be removed
-3[C4]+7[C4]-7[G4]+5[G4]-5[G1]+7[G1]-7[H3]+2[H3]-2[H7]+7[H7]-7[F7]+6[F7]-6[F4]+3[F4]
- 7 can be removed from J2
- 7 can be removed from B7
- 7 can be removed from J7
- 6 can be removed from F1
- 6 can be removed from F2
- 3 can be removed from E4
Passo 13
Rectangle Elimination
valore: 82.5
categoria doc: Rectangle_Elimination
If +7[F1] then -7[F7] forcing +7[H7] which removes all 7s from Box 7, so F1 cannot be 7
Passo 14
XYZ Wing
valore: 196.4
categoria doc: XYZ_Wing
XYZ-Wing pattern. Hinge: F2 (1/7/9), wings A2 F1, therefore
- 1 can be removed from E2
Passo 15
Hidden Pair
valore: 32.5
categoria doc: Hidden_Candidates
Hidden Pair 1/7 in Col 2, on cells {A2|F2}
- removes 9 from F2
Passo 16
Hidden Singles
valore: 3.2
categoria doc: Getting_Started
9 in F1 is last in row/box
Passo 17
X-Cycle
valore: 235.2
categoria doc: X_Cycles
X-CYCLE on 7 (Discontinuous Alternating Nice Loop, length 8):
+7[A1]-7[A2]+7[F2]-7[F7]+7[H7]-7[H3]+7[G1]-7[A1]
- Contradiction: When A1 is set to 7 the chain implies it cannot be 7 - it can be removed
Passo 18
XY-Chain
valore: 264.2
categoria doc: XY_Chains
length=6, chain ends: G1 and C9
This proves 5 is the solution at one or possibly both ends of the chain
-5[G1]+7[G1]-7[H3]+2[H3]-2[H7]+7[H7]-7[F7]+6[F7]-6[B7]+4[B7]-4[C9]+5[C9]
- 5 can be removed from C1
Passo 19
Pointing Pairs
valore: 45.8
categoria doc: Intersection_Removal
Pair: between Box 1 and Col 2:
- 5 can be removed from H2
- 5 can be removed from J2
Passo 20
Y-Wing
valore: 121
categoria doc: Y_Wing_Strategy
Y-Wing pattern. Hinge: H2 (8/9), wings B2 H8, therefore
- 5 can be removed from B8
Passo 21
Pointing Pairs
valore: 45
categoria doc: Intersection_Removal
Pair: between Box 3 and Col 9:
- 5 can be removed from J9
Passo 22
XY-Chain
valore: 279.6
categoria doc: XY_Chains
length=7. This XY-Chain is continuous and one value in each cell must be the solution, so all off-chain candidates can be removed
-6[E4]+5[E4]-5[G4]+7[G4]-7[G1]+5[G1]-5[H1]+8[H1]-8[H2]+9[H2]-9[J2]+2[J2]-2[E2]+6[E2]
- 6 can be removed from E1
- 6 can be removed from E8
Passo 23
Naked Pair
valore: 14.6
categoria doc: Naked_Candidates
Naked Pair 1/4 on cells {A1|E1} means
- 4 can be removed from D1
Passo 24
XY-Chain
valore: 214.6
categoria doc: XY_Chains
length=5, chain ends: E8 and F4
This proves 3 is the solution at one or possibly both ends of the chain
-3[E8]+4[E8]-4[E1]+1[E1]-1[F2]+7[F2]-7[F7]+6[F7]-6[F4]+3[F4]
- 3 can be removed from E6
- 3 can be removed from F9
Last candidate 5 in E6 changed to solution
Passo 25
Naked Singles
valore: 1.3
categoria doc: Getting_Started
Last candidate 6 in E4 changed to solution
Last candidate 7 in J6 changed to solution
Passo 26
Naked Singles
valore: 1.2
categoria doc: Getting_Started
Last candidate 3 in C6 changed to solution
Last candidate 2 in E2 changed to solution
Last candidate 3 in F4 changed to solution
Last candidate 5 in G4 changed to solution
Passo 27
Naked Singles
valore: 1
categoria doc: Getting_Started
Last candidate 7 in C4 changed to solution
Last candidate 7 in G1 changed to solution
Last candidate 9 in J2 changed to solution
Passo 28
Naked Singles
valore: 0.8
categoria doc: Getting_Started
Last candidate 6 in D1 changed to solution
Last candidate 8 in H2 changed to solution
Last candidate 2 in H3 changed to solution
Last candidate 4 in J9 changed to solution
Passo 29
Naked Singles
valore: 0.6
categoria doc: Getting_Started
Last candidate 5 in B2 changed to solution
Last candidate 8 in C1 changed to solution
Last candidate 5 in C9 changed to solution
Last candidate 5 in H1 changed to solution
Last candidate 7 in H7 changed to solution
Last candidate 2 in J7 changed to solution
Last candidate 5 in J8 changed to solution
Passo 30
Naked Singles
valore: 0.6
categoria doc: Getting_Started
Last candidate 6 in C2 changed to solution
Last candidate 4 in C5 changed to solution
Last candidate 6 in F7 changed to solution
Last candidate 9 in H8 changed to solution
Passo 31
Naked Singles
valore: 0.5
categoria doc: Getting_Started
Last candidate 8 in B5 changed to solution
Last candidate 4 in B7 changed to solution
Passo 32
Hidden Singles
valore: 0.8
categoria doc: Getting_Started
2 in D9 is last in row/column/box
6 in B8 is last in row/column/box
9 in A9 is last in row/column/box
Passo 33
Bi-value Universal Grave
valore: 20.6
categoria doc: BUG
BUG+1 found in A3, 7 must be the solution
All other incomplete cells contain two candidates apart from A3. Other candidates in A3 would lead to zero, two or more solutions so they can be removed.
Last candidate 7 in A3 changed to solution
Passo 34
Naked Singles
valore: 0.1
categoria doc: Getting_Started
Last candidate 1 in A2 changed to solution
Last candidate 3 in A8 changed to solution
Last candidate 3 in B3 changed to solution
Last candidate 4 in D3 changed to solution
Passo 35
Naked Singles
valore: 0
categoria doc: Getting_Started
Last candidate 4 in A1 changed to solution
Last candidate 7 in B9 changed to solution
Last candidate 7 in D8 changed to solution
Last candidate 1 in E1 changed to solution
Last candidate 4 in E8 changed to solution
Last candidate 7 in F2 changed to solution
Passo 36
Naked Singles
valore: 0
categoria doc: Getting_Started
Last candidate 3 in E9 changed to solution
Last candidate 1 in F9 changed to solution