## Anti-knight Ferz-non-consecutive

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Anti-knight Ferz-non-consecutive

I was fiddling around with JSudoku and ended up finding this variant. Unfortunately, I am having no luck in solving it at all. Is anyone skilled enough to solve this puzzle without branching? Could you show what I have missed?

Puzzle rules:

1. Normal sudoku rules apply
2. Anti-knight - no number can be a knights move away from itself.
3. Ferz-non-consecutive - no consecutive numbers can be diagonally adjacent.

Code: Select all
`..9|...|7.....|...|...7..|...|..9---+---+---...|.8.|......|6.2|......|.4.|...---+---+---3..|...|..4...|...|.....5|...|8..`

As a side note: Is 12 clues the minimum number of clues for this variant?
primeprover

Posts: 4
Joined: 21 December 2015

### Re: Anti-knight Ferz-non-consecutive

I will be able to give you a comprehensive answer in 48h

Watch this space!

Tarek

tarek

Posts: 3745
Joined: 05 January 2006

### Re: Anti-knight Ferz-non-consecutive

JSudoku won't give me a solution, it said multiple solutions.

But my solver gave single solution:
Hidden Text: Show
Code: Select all
`2 8 9 1 3 4 7 6 51 5 4 9 6 7 2 3 87 6 3 2 5 8 1 4 99 7 6 3 8 1 4 5 25 4 1 6 7 2 9 8 38 3 2 5 4 9 6 7 13 2 7 8 9 6 5 1 44 9 8 7 1 5 3 2 66 1 5 4 2 3 8 9 7`

Required 4 levels of chains/nets. Hard but not that hard. Rating should be around SE 9.0 or lower.
creint

Posts: 201
Joined: 20 January 2018

### Re: Anti-knight Ferz-non-consecutive

primeprover wrote:I was fiddling around with JSudoku and ended up finding this variant. Unfortunately, I am having no luck in solving it at all. Is anyone skilled enough to solve this puzzle without branching? Could you show what I have missed?

This is an extremely tough puzzle. I modified Sukaku Explainer to support Ferz NC and with the set of techniques available it couldn't solve it (the solver still needs some tweaking but overall I think still a difficult puzzle). I confirm the unique solution that creint has also mentioned.

Solvable is the following:
Code: Select all
`............5..........65...9....1.............5....9...12..........1............`

primeprover wrote:As a side note: Is 12 clues the minimum number of clues for this variant?
No.
Code: Select all
`.................................3.............6.........9............7..........`

tarek

Posts: 3745
Joined: 05 January 2006

### Re: Anti-knight Ferz-non-consecutive

Thanks for having a look. It looks like this puzzle is hard enough that an extreme amount of effort is needed to find a solution. This is beyond a lot of solvers(without recursion) including humans.

JSudoku gave me the unique solution after recursively solving.
primeprover

Posts: 4
Joined: 21 December 2015

### Re: Anti-knight Ferz-non-consecutive

I generated a few & rated them with an un-released version of sukaku explainer:
Here is one that is solvable & SE rates it at ER=3.2 (X-Wing)
Code: Select all
`...3..........9........6...4.....67...........58.....1...6........9..........7...`

tarek

Posts: 3745
Joined: 05 January 2006

### Re: Anti-knight Ferz-non-consecutive

Nice puzzle

Early on I used a couple of FNC/AN interactions that I thought neat and hoped to avoid the x-wing, but as I plodded on there it was.

I remember making quite a few of these early on (probably as killers) as I found NC/AN too restrained.
HATMAN

Posts: 271
Joined: 25 February 2006
Location: Nigeria

### Re: Anti-knight Ferz-non-consecutive

HATMAN wrote:Nice puzzle

Early on I used a couple of FNC/AN interactions that I thought neat and hoped to avoid the x-wing, but as I plodded on there it was.

I remember making quite a few of these early on (probably as killers) as I found NC/AN too restrained.

thanks for the feedback, I'll post a few of these on the forbidden pairs thread in case there is an interest

tarek

tarek

Posts: 3745
Joined: 05 January 2006

### Re: AN FNC+ ER=3.6

Another fun to solve puzzle
This is an AN FNC+ (Ferz Non consecutive including 1,9 and Anti-kNight)
Code: Select all
`............9.5.............5.....1...........2.....5.............2.7............`

tarek

Posts: 3745
Joined: 05 January 2006

### Re: AN FNC+ ER=3.6 solution

Sukaku Explainer v1.17.7 has been released

It would solve/rate/analyze puzzles with Ferz non consecutive and Ferz non-consecutive +

Here is the analysis for the above FNC+ puzzle
Code: Select all
`Analysis resultsDifficulty rating: 3.6 (Generalized Naked Triplet)This Anti-kNight Ferz NC+ Sudoku can be solved using the following logical methods: 64 x Hidden Single1 x Direct Hidden Pair8 x Naked Single1 x Non-Consecutive Forcing Cell16 x Locked Non Consecutive13 x Generalized Intersections1 x Generalized Naked TripletThe most difficult technique (ER): Generalized Naked Triplet`

solution: Show
Code: Select all
`432871965871965432965432871654328719719654328328719654287196543543287196196543287`

Tarek