## Frameless Non-Consecutive

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Frameless Non-Consecutive

Frameless NC 1

I really like para's idea here. to me it is a bit like a Frame Kimo but much more interesting.

I still have not solved para's original one yet and have had difficulty downloading the others he pointed out. So I decided to create one myself for two reasons:

1 to help me learn how to solve them (I've avoided looking at the walkthroughs so far)

2 it is a great puzzle type: so we need puzzles that are not just for the top guys.

In order to make them easier you need at least one added constraint, for the first one I've chosen {plain} Non-Consecutive. (For the next one I'll try Windoku X and probably diagonal repeat after that.)

Note I did not use the red clues in my solution but I left them in for symmetry and to allow for an easier puzzle if you wish. I also think it should be solvable without the left r456 totals.

HATMAN

Posts: 276
Joined: 25 February 2006
Location: Saudi Arabia

### Re: Frameless Non-Consecutive

In addition to the original one he made 2 extra ones, a 6x6 and another 9x9. They are available from the following link:

Here are the links to the puzzle images: (I hope Para would not oppose me for linking them here. )

6x6

9x9

By the way thanks for the new puzzles. Looks like a lot of fun and will certainly do them when time allows.

simon_blow_snow

Posts: 85
Joined: 26 December 2010

### Re: Frameless Non-Consecutive

Thanks Simon

I've been having difficulty with the frameless windoku X so I've moved on to the frameless repeat. This is going well and I hope to be able to post in the middle of the week.

With a frameless repeat the cages are all diagonal so you have the choice of going widdershins or deisul. I've gone for maximum repeat which limits thing significantly, but has the problem that I my not get the best solution. On one of these maximum repeats a few years ago udosuk managed to beat my solution.

Cheers

Maurice
HATMAN

Posts: 276
Joined: 25 February 2006
Location: Saudi Arabia

### Re: Frameless Non-Consecutive

I've written a complete walkthrough for this puzzle. This time I did'nt used all clues to solve it, but only 18 out of the 30 clues given. And it isn't even the minimal requirement. From my approximation, perhaps 12 or even 11 clues are enough for a unique solution.

Here is a text format of the puzzle grid, showing the clues I used:

Code: Select all
`   07 12 10             06 12  +--+--+--+--+--+--+--+--+--+06|        |        |        |08  |        |        |        |1015|        |        |        |  +--+--+--+--+--+--+--+--+--+  |        |        |        |  |        |        |        |  |        |        |        |  +--+--+--+--+--+--+--+--+--+  |        |        |        |14  |        |        |        |0809|        |        |        |11  +--+--+--+--+--+--+--+--+--+   14 04             11 12 07`

Here is the complete walkthrough (6 steps): Show
Step 1:
L-R1(06): R1C1<>{789}
--> T-C1(07): max R12C1 = 7
T-C2(12): max R12C2 = 12
L-R3(15): max R3C12 = 15
--> N1: min R123C3 = 45-7-12-15 = 11
--> T-C3(10): R12C3 = 10(2) = {19/28/37/46}
--> N1: min R3C123 = 45-7-12-10 = 16
--> L-R3(15),NC: R3C12 = 15(2) = {69} (R3,N1)
--> T-C1(07),NC: R12C1 = 7(2) = {25} (C1,N1)
--> T-C3(10): R12C3 = 10(2) = {37} (C3,N1)
--> T-C2(12): R12C2 = 12(2) = {48} (C2,N1)
--> R3C3 = [1]
--> L-R1(06): R1C12 = 6(2) = [24]
--> NC: N1 = [247583961]

Step 2:
T-C8(06),NC: R1C8<>{1389}, must be [5/6]
--> NC: R1C79+R2C8<>{56}
R-R1(08),NC: R1C9<>{19}, must be [3/8]
--> T-C9(12): R2C9<>{26}
R-R2(10),NC: R2C9<>{47}, must be [1/9]
N3: [6] locked in R1C8+R2C7
--> NC: R2C8<>[7]
--> R-R2(10),NC: [9] locked in R2C89 = 10(2) = {19} (R2,N3)
--> R1C79={38} (R1,N3)
--> T-C9(12): R12C9 = 12(2) = [39]
--> R-R1(08) = 8(2) = [53]
--> R1C7=[8], R2C8=[1]
--> Hidden single N3: R2C7=[6]
NC: R2C4=[7]
--> R2C56={24} (N2)
--> NC: R3C56<>[3]
--> Hidden single N2: R3C4=[3]

Step 3:
B-C9(07),NC: R8C9<>{78}
--> R-R8(08): max R8C89 = 8
R-R7(14): max R7C89=14
R-R9(11): max R9C89=11
--> N9: min R789C7 = 45-8-14-11 = 12
--> B-C7(11): R89C7 = 11(2) = {29/47}
--> N9: min R7C789 = 45-11-8-11 = 15
--> R-R7(14): R7C89 = 14(2) = [68/86/95]
--> B-C8(12): R8C8<>{67}
--> R-R8(08),NC: R8C89 = 8(2) = [26/35]
--> NC: R7C89 = 14(2) = [68]
--> R8C89 = 8(2) = [35]
--> B-C8(12): R89C8 = 12(2) = [39]
--> R-R9(11): R9C89 = 11(2) =[92]
--> NC: R89C7 = 11(2) = [74]
--> R37C7=[21]

Step 4:
B-C2(04): R89C2 = 4(2) = [13]
--> L-R9(09): R9C12 = 9(2) = [63]
--> B-C1(14): R89C1 = 14(2) = [86]
--> NC: N7=[472819635]
--> NC: R9C456=[817]
--> NC: R8C6<>[6], must be [2/4]
--> NC: R7C6<>[3]
--> Hidden single N8: R7C5=[3]
--> NC: R8C5=[6]
--> NC: R1C456=[196]

Step 5:
NC: R6C89<>[7]
N6: [8] locked in R456C8
--> NC: R5C8<>[7]
N6: [6] locked in R456C9
--> NC: R5C9<>[7]
--> N6: [7] locked in R4C89 (R4)
--> NC: R4C89<>{68}
--> NC: R4C2=[9]
--> NC: R4C347=[465]
--> NC: R5C4<>[5]
--> R4: [8] locked in R4C56 (N5)

Step 6:
NC: R6C1<>[3], R6C5<>{24}
NC: R6C12 can't be [12], must include {57}
--> Complex naked pair {57} in R6C125 (R6)
--> Hidden single C4: R7C4=[5]
--> NC: N8 = [539264817]
--> N2 = [196742385]
--> R4 = [394628571]
--> R3C89=[47]
--> NC: R5 = [158473926]
--> R6 = [726951384]

247196853
583742619
961385247
394628571
158473926
726951384
472539168
819264735
635817492

simon_blow_snow

Posts: 85
Joined: 26 December 2010

### Re: Frameless Non-Consecutive

Beginner's question: What does "non-consecutive" mean in this context?

I suppose I could search earlier posts for an answer, but I'm lazy.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

### Re: Frameless Non-Consecutive

Bill

no horizontal or vertical pair of adjacent cells may contain two numbers that are consecutive.

MaURICE
HATMAN

Posts: 276
Joined: 25 February 2006
Location: Saudi Arabia