## The wheel (non consecutive)

For fans of Killer Sudoku, Samurai Sudoku and other variants

### The wheel (non consecutive)

Here is a non consecutive

No cell may include a number consecutive to any adjacent cell, any “neighbouring” cell. For example if R5C5 = 6, none of the 4 cells in R46C5 and R5C46 may be {57} (nor 6 of course).

....5......8...7...5.....9..........5...6...7..........1.....4...9...2......4....

Have fun
Jean-Christophe

Posts: 149
Joined: 22 January 2006

Here is my walkthrough in tiny text you may copy-paste to a text editor like note pad

Step 1
R7C8 = 4 -> R8C8 <> {35}, R8C7 = 2 -> R8C8 <> {13}
7 of N9 locked in R89C7 -> R89C7 <> {68}
-> R8C8 = 7

Step 2
R3C8 = 9 -> R3C79 <> 8, R2C7 = 7 -> R1C7 <> 8
-> 8 of N3 locked in R1C89, 8 of N2 locked in R3C456
-> R3C5 <> 7
R5C5 = 6 -> R46C5 <> 7
-> R7C5 = 7 (hidden single in C5)

Step 3
R7C5 = 7 -> R8C5 <> 8, R9C5 = 4 -> R8C5 <> 3
-> R8C5 = 1

Step 4
R2C3 = 8 -> R2C2 <> 9, R3C2 = 5 -> R24C2, R3C13 <> {46}
-> R2C2 = {23}, R4C2 = {23789}
7 of N7 locked in R9C123-> R9C2 <> {68} = {27}
R8C3 = 9 -> R8C2 <> 8
-> 8 of N7 locked in R789C1, 8 of N4 locked in R456C3
-> R5C2 <> 9 = {238}

Step 5
Either R5C2 = 8 -> R4C2 <> {789} = {23}
Or else R5C2 = {23}
-> R45C2 must hold one of {23}
This forms a complex naked pair on {23} with R2C2
-> not elsewhere in C2
-> R9C2 = 7, R8C2 = 4

Step 6
R2C3 = 8 -> R13C3 <> 7
7 of N1 locked in R123C1 -> R2C1 <> 6
R2C7 = 7 -> R2C68, R13C7 <> 6
5 of N3 locked in R2C89 -> R2C89 <> {46}
-> R2C4 = 6 (hidden single in R2)

Step 7
R3C9 = 6 (hidden single in R3)
-> R2C8 = 5
6 of N9 locked in R79C7, 6 of N6 locked in R46C8
7 of N2 locked in R13C6, 7 of N5 locked in R46C4 -> R5C4 <> 8

Step 8
R7C2 = 1 -> R7C13 <> 2
-> 2 of N7 locked in R9C13, 2 of N8 locked in R7C46
R9C5 = 4 -> R9C46 <> {35}, R9C4 = {89}, R9C6 = {689}
6 of N8 locked in R789C6 -> R8C6 <> 5
R9C46, R8C6 = naked triplet on {689}

Step 9
R7C4 = {235}, R8C4 = {35}
Either R8C4 = 5 or else R8C4 = 3 -> R7C4 <> {23} = 5
-> 5 of N8 locked in R78C4, 5 of N5 locked in R46C6 -> R5C6 <> 4
5 of R7 locked in R7C34 -> R7C3 <> 6 = {35}
R7C346 = naked triplet on {235}
R78C1 = {68} = nacked pair

Step 10
6 of R9 locked in R9C67 -> R9C7 <> 5 = {68}
R9C467 = naked triplet on {689} -> R9C9 = {135}
5 of N9 locked in R89C9, 5 of N6 locked in R46C6 -> R5C6 <> 4
5 of R6 locked in R6C67 -> R6C67 <> 4
5 of R4 locked in R4C67 -> R4C67 <> 4

Step 11
4 of N6 locked in R46C9, 4 of N3 locked in R13C7
R2C9 = {123} -> R1C9 <> 2
2 of N3 locked in R1C8, R2C9 -> R1C9 <> {13}
-> R1C9 = 8, R6C8 = 8, R7C9 = 9, R4C8 = 6, R6C7 = 5
R79C7 = [86], R78C1 = [68], R8C6 = 6
R4C6 = 5, R3C7 = 4, R2C6 = 4, R1C1 = 4
R1C6 = 7, R3C1 = 7
R1C7 = {13} -> R1C8 <> 2 -> R2C9 = 2
...

Unique solution :

496257318
138694752
752831496
927485163
584163927
361729584
613572849
849316275
275948631

Jean-Christophe

Posts: 149
Joined: 22 January 2006

No takers yet, I see.

When a puzzle starts out with NO singles, NO naked pairs, NO naked triples, and where there are at least three initial candidates for each cell (usually more), it's no wonder most of us ordinary mortals give up soon.

I think you should take it down a notch.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

Actually, I solved it, just didn't bother to post a reply with my computer having some problems...

You see JC also posted in other places and many others could have solved it...

BTW I think there is only 1 "tricky step" in the puzzle and the rest are (relatively) more trivial stuffs... Just that you might need to learn some good "non-cons" techniques before you tackle this puzzle....
udosuk

Posts: 2698
Joined: 17 July 2005

Reading some of Bill's messages, I noticed it is a usual complain from him, so I won't bother replying...

Anyhow, here is a grid especially designed for Bill, enough naked single ?

Code: Select all
`+-------+-------+-------+| . 2 . | 1 . 9 | . 8 . || 1 . 9 | . 8 . | 6 . 7 || . 8 . | 7 . 6 | . 5 . |+-------+-------+-------+| 8 . 6 | . 7 . | 5 . 1 || . 7 . | 9 . 5 | . 4 . || 5 . 1 | . 4 . | 2 . 3 |+-------+-------+-------+| . 3 . | 4 . 2 | . 1 . || 9 . 5 | . 3 . | 4 . 2 || . 6 . | 5 . 1 | . 3 . |+-------+-------+-------+`

PS It has a unique solution as a non consecutive sudoku, not as a regular sudoku.
Jean-Christophe

Posts: 149
Joined: 22 January 2006

Those not familiar with techniques for non consecutive may have a look here : http://sudoku.apinc.org/?p=139

And here : http://www.djape.net/sudoku/forum/viewtopic.php?p=2963#p2963
Jean-Christophe

Posts: 149
Joined: 22 January 2006