The New Sudoku Players' Forum

[Jean-Christophe]

Here is a killer where one of the nonets forms a magic square Each of the mini-row, mini-column and 2 mini diagonals of the magic square add up to the same sum.



3x3::k:3089:2322:2322:3861:4118:4118:4621:4621:4621:3089:3089:6661:3861:3861:4118:4621:8457:4366:2567:2567:6661:3861:6658:6658:6658:8457:4366:2567:6661:6661:6145:6145:6658:8457:8457:4366:2827:2827:8456:8456:6145:8457:8457:1546:1546:5135:8456:8456:4099:6145:6145:4100:4100:4358:5135:8456:4099:4099:4099:5652:4100:4358:4358:5135:8456:3852:4119:5652:5652:4100:3088:3088:3852:3852:3852:4119:4119:5652:3859:3859:3088:

Enjoy

[Jean-Christophe]

Here is a walktrough and the solution

One of the nonet = Magic Square (MS)

N2 <> MS because of Cage 15/4 (should have been 20/4)
N8 <> MS because of Cage 22/4 (should have been 20/4)
N5 <> MS because of Cage 24/5 (should have been 25/5)
N7 <> MS because of Cage 15/4 (should have been >= 16)
N9 <> MS because of Cage 15/2 (should have been <= 13)

Outies of N1 -> R4C123 = 12 -> N4 <> MS
Min R4C1 = 1 -> Max R4C23 = 11 -> Min R23C3 = 15 -> R23C3 = {6789}
-> N1 <> MS because R123C3 >= 16

Outies of N9 -> R6C789 = 15 (can be a MS)

Innies of N2 -> R3C56 = 14 = {59|68}
Outies of N2 -> R3C7+R4C6 = 12 = {39|48|57}

Innies of N8 -> R7C45 = 7 = {16|25|34}
Outies of N8 -> R6C4+R7C3 = 9

Outies of N1478 -> R56C4 = 10
Innies of N5 -> R45C6 = 11

MS is either N3 or N6

If MS = N3 -> R2C7 = 18-15 = 3, R2C9 = 7
Which gives :
48 19 26
3 5 7
48 19 26
Since R3C7+R4C6 = 12 -> R4C6 = {48} -> R3C56 = {59} -> R13C8 = [91]
Which gives :
4 9 2
3 5 7
8 1 6

If MS = N6 -> R5C89 = [51], R5C7 = 9
Which gives :
24 37 68
9 5 1
24 37 68

Either R3C8 = 1 or R5C9 = 1 -> R123C9, R456C8, Cage 33/6 within N56 <> 1
Either R1C9 = 2 or R46C7 = {24} -> R123C7, R456C9 <> 2
-> R5C89 = [24|51]

Either Cage 17/3 in C9 = [764] -> R4C9 = 4 or R46C7 = {24}
-> R5C89 <> [24] = [51]
MS = N6
R5C7 = 9
R46C7 = {24}, R46C8 = {37}, R46C9 = {68}

R3C7 <> {49} -> R45C6 <> {38}
Cage 26/4 in R3C567+R4C6 = {3689|4589|5678} = {8..} locked in R3C567 -> no 8 elsewhere in R3

R4C78 = [27|43] = 9|7 -> R23C7+R5C6 = 15|17 = {168|278} = {8..}
-> R2C8 = 8

Cage 15/5 in N9 = [69]

8 of Cage 26/4 locked in R3C56 = {68}
R1C8 = 6 (hidden single)

R6C78 = [27|43] = 9|7
8 of N9 locked in R78C7 -> Min R78C7 = {18} = 9 -> Max R6C78 = 7 = Min
-> R78C7 = {18}, R6C789 = [438]
R4C789 = [276]
R3C8 = 1, R5C6 = 6, R4C6 = 5
R3C567 = [687]
R12C7 = {35}, R1C9 = 4, R23C9 = {29}

R3C3 = 9, R23C9 = [92]
Split cage 12/3 in R4C123 = {138}
R4C1 = 1, R4C23 = {38}, R2C3 = 6, R3C12 = {45}, R3C4 = 3
R4C45 = {49}, Cage 11/2 in R5C12 = {47}
Split cage 10/2 in R56C4 = [82], R5C35 = [23]
R7C3 = 7, Split cage 7/2 in R7C45 = [61], R6C56 = [71]
...


Solution:
218957364
376124589
459368712
183495276
742836951
695271438
937612845
564789123
821543697