## Extra Groups Killer Sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Extra Groups Killer Sudoku

This is the 14th puzzle I've made with this variation (I've been posting them in DJape's forums)

Rules:
Fill in the numbers 1-9 so that they appear exclusively in each row, column, nonet, and diagonal.
The numbers 1-9 must also appear exclusively in the colored extra groups regions.
The cages represent sums just as they would in any killer sudoku puzzle.
h3lix

Posts: 8
Joined: 04 December 2006

Nice interplay of LoL and sum cages
Here is my walkthrough and the solution. Not sure all steps are needed

45 on central EG -> R4C4+R6C6 = 15 = {69|78}

LoL on N1 -> {R1C3,R2C23} = {R3C4,R4C23}
Cage 24/5 in N14 and EG -> whichever digits go in R4C23 can't go in R2C3 nor R3C4
-> {R4C23} = {R1C3,R2C2} -> R2C3 = R3C4
Because {R4C23} = {R1C3,R2C2} are locked in C23, they form a double X-Wing
-> R1C3 = R4C2, R2C2 = R4C3
-> two cells of R789C1 = R4C23

LoL on N12 -> {R4C23} = {R3C56}
LoL on N4 -> {R4C23} = {R56C4}
Thus {R4C23} = {R1C3,R2C2} = {R3C56} = {R56C4}

45 on N1 -> R4C23 - R1C3 = 24+24 - 45 = 3
Since {R4C23} = {R1C3,R2C2} -> R1C3+R2C2 - R1C3 = 3 -> R2C2 = 3
R4C3 = 3
3 locked in R3C56, R56C4

Cage 16/2 in R1C89 = {79}
R1C7 = 3 (hidden single in R1)

Interaction of LoL and cages:
Since {R4C23} = {R56C4} and R2C3 = R3C4
-> R3C23 - R4C4 = 24-20 = 4
Since R4C4 = {6..9} -> R3C23 = 10..13

LoL on R12 -> {R1C12,R2C1} = {R3C789}
Since R3C89 = 7 = {16|25} -> Cage 24/5 in N1 = {13569|23568} = {56..}
-> no {56} elsewhere in N1, EG
-> R2C3 = R3C4 = {27}
R4C2 = {124}, R56C4 = R3C56 = {1234}
{47} of EG or N1 locked in Cage 24/5 in N14 = {13479|23478}

Similarly for symmetry
-> R8C8 = 18+32-45 = 5
R6C7 = 5
5 locked in R45C6, R7C45

R9C2 <> 3 -> R9C1 <> 5
-> R4C6 = 5 (hidden single in D/)
Cage 17/4 in C6 = {1259|1457|2456} -> R6C6 = {679}, R57C6 = {124}
-> R6C8 = {124}, R89C7 = {124}, R4C4 = {689}

Cage 20/4 in C4 = {1379|2378|3467} = {7..}
-> R3C4 = 7, R2C3 = 7

Cage 22/3 in N2 = {589}
R7C4 = 5 (hidden single in C4)

LoL on R12 -> {R1C12,R2C1} = {R3C789}
Cage 24/5 in N1 & Cage 7/2 in N3 -> R3C1 = 24-3-7-R3C7
-> R3C1 = 14-R3C7 -> R3C17 = 14 = {68}

-> Cage 7/2 in R3C89 = [25]
Cage 24/5 in N1 = {23568}
Cage 24/5 in N14 = {13479}
R4C2 = R1C3 = {14}
R3C56 = R56C4 = {134}

R56C4&R5C6 = naked triplet on {134} -> not elsewhere in N5
-> R5C123 <> {134} (either in same EG or same row)
2 of N5 locked in R456C5 -> not elsewhere in C5

Cage 20/4 in C4 = {1379|3467} -> R4C4 = {69}
-> R4C4+R6C6 = {69}, naked pair -> not elsewhere in C5, N5, EG, D\
R456C5 = {278}, naked triplet -> not elsewhere in C5, N5, EG, Cage 30/7
-> R1C5 = 5, R2C56 = [98]
R2C14 = [52], R3C17 = [68], R3C2 = 9

Outies of C5 -> R3C6+R8C4 = 11
-> R3C6 = 3, R8C4 = 8, R89C5 = {36}

Cage 17/4 in C6 = {1259|2456} = {2..}
-> R7C6 = 2, R8C7 = 2

LoL on R89 -> R7C123 = R8C9+R9C89
Cage 32/5 in N9 & Cage 12/2 in N7 -> R7C9 = 32-5-12-R7C3 = 15-R7C3
-> R7C39 = 15 = {69}
Cage 12/2 in R7C12 = {48}
R7C5 = R9C7 = R6C8 = R5C6 = 1
R3C5 = R1C3 = R4C2 = 4, R56C4 = {34}
R3C3 = 1, R4C1 = 1, R8C2 = 1, R1C46 = [16], R2C9 = 1
R4C4 = 6, R6C6 = 9, R7C78 = [73]
...

Solution
+-------+-------+-------+
| 8 2 4 | 1 5 6 | 3 9 7 |
| 5 3 7 | 2 9 8 | 4 6 1 |
| 6 9 1 | 7 4 3 | 8 2 5 |
+-------+-------+-------+
| 1 4 3 | 6 8 5 | 9 7 2 |
| 9 7 5 | 3 2 1 | 6 4 8 |
| 2 6 8 | 4 7 9 | 5 1 3 |
+-------+-------+-------+
| 4 8 9 | 5 1 2 | 7 3 6 |
| 7 1 6 | 8 3 4 | 2 5 9 |
| 3 5 2 | 9 6 7 | 1 8 4 |
+-------+-------+-------+
Jean-Christophe

Posts: 149
Joined: 22 January 2006