## 4x4 Killer Su-Doku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### 4x4 Killer Su-Doku

I am very interested in small Killer Su-Dokus and I have created some 4x4 Killer Su-Dokus.

This is the first one:
Code: Select all
`.. 18 18 03.. 15 18 1815 15 18 1815 15 15 15`

06 06 indicates a 2-cell cage totaling 6.
I have not found a 4x4 Killer Su-Doku harder than this. Please let me know if you have.

This is the second one:
Code: Select all
`16 16 16 16.. 16 16 16   ------16 16 16 ..16 .. 16 ..`

The dashes show the dividing line between the two cages. There are only two cages in this puzzle, and I think that this is the minimum. It is also the only puzzle that I have found where every cage adds up to the same number.

What do you think of my puzzles?
Hidden Text: Show
Once upon a time I was a teenager who was active on here 2007-2011
999_Springs

Posts: 367
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

Interesting puzzles, a couple of points:

The convention for the last year or so has been to only have cages with no repeats. How many cages would you need with this restriction?

We have got down to a puzzle with one given: see

http://www.djape.net/sudoku/forum/viewtopic.php?t=938&postdays=0&postorder=asc&start=30
HATMAN

Posts: 205
Joined: 25 February 2006

### Re: 4x4 Killer Su-Doku

999_Springs wrote:I have not found a 4x4 Killer Su-Doku harder than this. Please let me know if you have.
...
What do you think of my puzzles?

I wouldn't call your puzzles "hard", but it's almost impossible to compare to others because you might be the only soul in the universe who're creating 4x4 killers allowing repetition in cages (there are others making 4x4 killers and others making 9x9 allowing repetition in cages, but not likely both )...

999_Springs wrote:
Code: Select all
`.. 18 18 03.. 15 18 1815 15 18 1815 15 15 15`

A 3-step walkthrough:

1. Innies of whole grid: r12c1=40-3-15-18=4=[13]
2. Outies of block 2: r1c2+r3c34=18+3-10=11=4+7 => r1c2=4, r3c34=[34]
3. r1c3=2, r2c234=[241], r3c12=[21], r4c1234=[4312]

1423
3241
2134
4312

999_Springs wrote:
Code: Select all
`16 16 16 16.. 16 16 16   ------16 16 16 ..16 .. 16 ..`

Another 3-step walkthrough:

1. Innies of blocks 1,2: r2c1=20-16=4
2. Innies of blocks 3,4: r3c4+r4c24=20-16=4=1+3 => r3c4=1, r4c24=[12]
3. r12c4=[43], r4c13=[34], r3c12=[24], r2c23=[21], r1c123=[132], r3c123=[243]

1324
4213
2431
3142

udosuk

Posts: 2698
Joined: 17 July 2005

udosuk wrote:
you might be the only soul in the universe who're creating 4x4 killers allowing repetition in cages

Should I start a production line then!!?

udosuk wrote:
1. Innies of whole grid: r12c1=40-3-15-18=4=[13]
2. Outies of block 2: r1c2+r3c34=18+3-10=11=4+7 => r1c2=4, r3c34=[34]
3. r1c3=2, r2c234=[241], r3c12=[21], r4c1234=[4312]

You forgot the single in r1c4. So it should be a 4-step walkthrough.
Hidden Text: Show
Once upon a time I was a teenager who was active on here 2007-2011
999_Springs

Posts: 367
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

999_Springs wrote:
udosuk wrote:1. Innies of whole grid: r12c1=40-3-15-18=4=[13]
2. Outies of block 2: r1c2+r3c34=18+3-10=11=4+7 => r1c2=4, r3c34=[34]
3. r1c3=2, r2c234=[241], r3c12=[21], r4c1234=[4312]

You forgot the single in r1c4. So it should be a 4-step walkthrough.

No, firstly it's not a single but a given, secondly even if I wanted to add that assignment I'd have done it in step 3, just replacing "r1c3=2" with "r1c34=[23]".

So all in all they're 3-step puzzles...

I recently discovered that 4x4 Sudokus can be useful to real-life problems too, check out this thread...
udosuk

Posts: 2698
Joined: 17 July 2005

Eureka! A ONE-cage 4x4 Su-Doku!!!

Forget what I previously mentioned about the minimum number of cages in a 4x4 Killer Su-Doku. I have found a 4x4 Killer Su-Doku with only one cage.
Code: Select all
`.. 10 10 .... 10 10 10.. .. 10 .... .. .. ..`

Note: You don't even need the block constraint to solve the puzzle.

Now that I have found a 4x4 Killer Su-Doku with one cage, now I shall look for one with zero cages! My attempts at creating a 0-cage Su-Doku have not produced anything so far.

So I will decide to go even smaller: make Killer Su-Dokus out of 3x3 Latin squares. This is my first attempt:
Code: Select all
`14 14 14.. 14 .... 14 14`
Hidden Text: Show
Once upon a time I was a teenager who was active on here 2007-2011
999_Springs

Posts: 367
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

Interesting work. Congrats for working out the 1-cage puzzles. I won't comment on their difficulties but great discoveries indeed...

I don't think a valid Sudoku can be found with no clue and no cage at all (you need some info to fix the rotation/reflection order of the grid)...

However, other puzzles which have no clue and no cage but irregularly shaped "blocks" are possible.

For example, with Ripple Effect, it's possible to construct puzzles with 0 & 1 clue only:

Full credit to Dan Adams (h3lix), who produced these marvelous puzzles...
udosuk

Posts: 2698
Joined: 17 July 2005