Passi risolutivi (36)
Passo 1
Hidden Singles
valore: 5.9
categoria doc: Getting_Started
1 in H2 is last in column
2 in D1 is last in row/box
8 in C8 is last in column
8 in F9 is last in row/box
Passo 2
Hidden Singles
valore: 5
categoria doc: Getting_Started
1 in B8 is last in column
1 in E1 is last in column/box
1 in J9 is last in row/box
5 in G8 is last in column
7 in F5 is last in row
8 in A5 is last in row/box
8 in J4 is last in column
Passo 3
Hidden Singles
valore: 4
categoria doc: Getting_Started
1 in A6 is last in row/box
1 in D5 is last in column
5 in A9 is last in row
5 in E5 is last in row
5 in F1 is last in column/box
8 in G3 is last in row/column/box
Passo 4
Hidden Singles
valore: 3.7
categoria doc: Getting_Started
5 in C4 is last in row/column/box
Passo 5
Pointing Pairs
valore: 53.6
categoria doc: Intersection_Removal
Pair: between Box 5 and Row D:
- 6 can be removed from D8
- 6 can be removed from D9
Last candidate 7 in D8 changed to solution
Passo 6
Naked Singles
valore: 1.7
categoria doc: Getting_Started
Last candidate 6 in H8 changed to solution
Passo 7
Hidden Singles
valore: 3.3
categoria doc: Getting_Started
6 in D4 is last in column
Passo 8
Pointing Pairs
valore: 47.9
categoria doc: Intersection_Removal
Pair: between Box 9 and Row G:
- 7 can be removed from G1
Passo 9
Pointing Pairs
valore: 47.5
categoria doc: Intersection_Removal
Pair: between Box 5 and Col 6:
- 9 can be removed from G6
Passo 10
Rectangle Elimination
valore: 78.4
categoria doc: Rectangle_Elimination
If +3[H3] then -3[H4] forcing +3[F4] which removes all 3s from Box 4, so H3 cannot be 3
Passo 11
3D Medusa
valore: 246.5
categoria doc: 3D_Medusa
(RULE 5): Uncoloured candidate 3 in H1 can see coloured 3 elsewhere and an oppositely coloured 7 in its own cell. It can be removed.
(RULE 5): Uncoloured candidate 9 in G2 can see coloured 9 elsewhere and an oppositely coloured 2 in its own cell. It can be removed.
Passo 12
Line/Unit Reduction
valore: 60
categoria doc: Intersection_Removal
Line/Box Reduction: 3s in box 8 remove the following in the same box:
- 3 can be removed from G5
- 3 can be removed from G6
- 3 can be removed from J5
Passo 13
Fireworks
valore: 294.4
categoria doc: Fireworks
Triple Fireworks: The three cells [A7|A2|G2] are a locked set that must contain {2/4/6} therefore
- 7 can be removed from A7
- 3 can be removed from G2
Passo 14
Pointing Pairs
valore: 43.7
categoria doc: Intersection_Removal
Pair: between Box 3 and Row C:
- 7 can be removed from C1
Passo 15
Aligned Pair Exclusion
valore: 400.6
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 G1 / G2 reduced from 3/4/6/9->4/6/9 and 2/4/6->2/6
- Pair 2/3 found in ALS {J3}
- Combinations of 3/4/6/7 found in ALS {G6,G7,G9}
Note: some ALSs share cells and cannot be fully colour indicated
Passo 16
Hidden Pair
valore: 28.1
categoria doc: Hidden_Candidates
Hidden Pair 3/7 in Row G, on cells {G7|G9}
- removes 4 from G7
- removes 4 from G9
Passo 17
Hidden Singles
valore: 2.8
categoria doc: Getting_Started
4 in J7 is last in box
Passo 18
Pointing Pairs
valore: 38.4
categoria doc: Intersection_Removal
Pair: between Box 7 and Col 1:
- 4 can be removed from A1
- 4 can be removed from C1
Passo 19
Hidden Singles
valore: 2.5
categoria doc: Getting_Started
4 in A2 is last in row
Passo 20
Naked Triple
valore: 47.9
categoria doc: Naked_Candidates
Naked Triple 2/3/6 on cells {G2|J1|J3} means
- 6 can be removed from G1
Passo 21
X-Cycle
valore: 177.4
categoria doc: X_Cycles
X-CYCLE Rule 3 (Discontinuous Alternating Nice Loop, length 8):
+6[B7]-6[A7]+6[A1]-6[J1]+6[G2]-6[G6]+6[B6]-6[B7]
- Contradiction: When B7 is set to 6 the chain implies it cannot be 6 - it can be removed
Passo 22
X-Cycle
valore: 175.4
categoria doc: X_Cycles
X-CYCLE Rule 3 (Discontinuous Alternating Nice Loop, length 8):
+6[B9]-6[A7]+6[A1]-6[J1]+6[G2]-6[G6]+6[B6]-6[B9]
- Contradiction: When B9 is set to 6 the chain implies it cannot be 6 - it can be removed
Passo 23
XY-Chain
valore: 150.2
categoria doc: XY_Chains
length=4. This XY-Chain is continuous and one value in each cell must be the solution, so all off-chain candidates can be removed
-6[A1]+7[A1]-7[A3]+2[A3]-2[J3]+3[J3]-3[J1]+6[J1]
- 6 can be removed from C1
Passo 24
XY-Chain
valore: 146.6
categoria doc: XY_Chains
length=4, chain ends: J1 and G6
This proves 6 is the solution at one or possibly both ends of the chain
-6[J1]+3[J1]-3[C1]+9[C1]-9[G1]+4[G1]-4[G6]+6[G6]
- 6 can be removed from G2
- 6 can be removed from J5
Last candidate 2 in G2 changed to solution
Last candidate 2 in J5 changed to solution
Passo 25
Naked Singles
valore: 1
categoria doc: Getting_Started
Last candidate 3 in J3 changed to solution
Passo 26
Naked Singles
valore: 0.9
categoria doc: Getting_Started
Last candidate 9 in E3 changed to solution
Last candidate 6 in J1 changed to solution
Passo 27
Naked Singles
valore: 0.8
categoria doc: Getting_Started
Last candidate 7 in A1 changed to solution
Last candidate 3 in F2 changed to solution
Last candidate 7 in H3 changed to solution
Passo 28
Naked Singles
valore: 0.7
categoria doc: Getting_Started
Last candidate 2 in A3 changed to solution
Last candidate 4 in F4 changed to solution
Passo 29
Naked Singles
valore: 0.6
categoria doc: Getting_Started
Last candidate 6 in A7 changed to solution
Last candidate 9 in F6 changed to solution
Last candidate 3 in H4 changed to solution
Passo 30
Naked Singles
valore: 0.5
categoria doc: Getting_Started
Last candidate 3 in D6 changed to solution
Last candidate 3 in E7 changed to solution
Passo 31
Naked Singles
valore: 0.4
categoria doc: Getting_Started
Last candidate 9 in D9 changed to solution
Last candidate 6 in E9 changed to solution
Last candidate 7 in G7 changed to solution
Passo 32
Naked Singles
valore: 0.3
categoria doc: Getting_Started
Last candidate 4 in B9 changed to solution
Last candidate 9 in C7 changed to solution
Last candidate 3 in G9 changed to solution
Passo 33
Naked Singles
valore: 0.2
categoria doc: Getting_Started
Last candidate 6 in B6 changed to solution
Last candidate 2 in B7 changed to solution
Last candidate 3 in C1 changed to solution
Last candidate 6 in C2 changed to solution
Last candidate 7 in C9 changed to solution
Passo 34
Naked Singles
valore: 0.1
categoria doc: Getting_Started
Last candidate 9 in B2 changed to solution
Last candidate 3 in B5 changed to solution
Last candidate 4 in C5 changed to solution
Last candidate 4 in G6 changed to solution
Passo 35
Naked Singles
valore: 0
categoria doc: Getting_Started
Last candidate 9 in G1 changed to solution
Last candidate 9 in H5 changed to solution
Passo 36
Naked Singles
valore: 0
categoria doc: Getting_Started
Last candidate 6 in G5 changed to solution
Last candidate 4 in H1 changed to solution