## A couple killers I put together

For fans of Killer Sudoku, Samurai Sudoku and other variants

### A couple killers I put together

...are posted on my blog at

http://www.ndorward.com/blog/?p=64
and
http://www.ndorward.com/blog/?p=66

They're the first ones I've devised so don't be too critical ..... It took a while for me to figure out how to create these without constantly running into impossible situations or leaving "flipflop" cells that allowed for multiple answers. A very interesting exercise. I was trying to make them reasonably hard: I'd be interested to know how long it takes people here to solve them.
nd

Posts: 28
Joined: 11 September 2005

Had a go at the second (symmetrical) one - very nice! 26mins for me (longer than the Times killers have ever taken me) - it was fun, never felt trivial and I didn't sit there completely stuck for too long either. Needed a range of techniques. Seeing as there were some points when I was using relatively convoluted logic, I was constantly petrified that I would get to the last few boxes and find that I'd screwed it up by making too many assumptions. Luckily, it all worked out. By the way, are you using the rule that a digit cannot be repeated within a dotted shape, as the Times do? Certainly this puzzle fits it, but I wasn't sure if that might just be coincidence.

Haven't looked at the other one yet, though at a quick glance it looked harder to get going. Better not get distracted onto it for now, but I'll have a look at it at some point.

How do you go about composing them? Do you have a route for the solution in mind, or do you come up with something that has a unique solution, without much idea in advance of what needs to be done to solve it? If it's the latter then I'm amazed at how neat it turns out.

Great stuff.

Chris
ChrisT

Posts: 36
Joined: 16 October 2005

Hmm, didn't take me long to get tempted by the other one! Much the same things to say about it - took me roughly the same time (forgot to start my watch right at the start so can't be exact). Starting off was slightly tricky, but got through it with a bit of thought. Don't think it loses much through being asymmetrical, though obviously symmetrical is pretty if you can get it to work out.

I think the main thing that these two puzzles have over the times ones is that they are much less reliant on simple forced combinations, such as 16=9+7, 3=1+2 etc, though these are present in more complicated forms (eg 22 across 3 cells must contain a 9).

Keep them coming.

Chris
ChrisT

Posts: 36
Joined: 16 October 2005

Had a go at the first one, surreptitiously while at work

Now either I've done something wrong (which is more than possible, especially as ChrisT seems to have managed it ) or this one has two solutions and a duplication of 5 in the 27 cage overlapping boxes 4 and 5, which in theory isn't allowed. Spent about 30 minutes on and off.

My solution came out as follows:

Code: Select all
`7 6 9 3 2 4 5 8 13 1 4 6 8 5 7 9 25 2 8 1 7 9 3 6 41 9 7 2 6 8 4 5 38 3 [56] [59] 4 1 2 7 [69]2 4 [56] [59] 3 7 8 1 [69]4 7 3 8 1 6 9 2 89 5 1 4 5 2 6 3 76 8 2 7 9 3 1 4 5`

The options for rows 5 and 6 are interchangeable i.e. could be .. 5 9 .... 6 or .. 6 5 .... 9.

Will have a go at second puzzle shortly
CathyW

Posts: 316
Joined: 20 June 2005

Quickly comparing your solution to mine, it's mostly the same but a couple of differences. However, I think your "35" box adds up to 33. I think probably if you replace r6c5 with a 5, the rest sorts itself out.

Chris
ChrisT

Posts: 36
Joined: 16 October 2005

You are quite right Chris, many thanks - but where does 3 go in column 5 and where does 5 go in column 4?!

Well done to nd for creating a nicely challenging puzzle.
CathyW

Posts: 316
Joined: 20 June 2005

You need to switch a few other things around in your solution to make it all fit. I always find it's incredibly hard, if not impossible, to rearrange things once you have discovered a mistake, short of starting right back at the beginning. Even though, when you look back on it, there may only be a few things that needed changing. This is the solution I got:

Code: Select all
`769234581314865792528179364197628453835941276246357819473516928951482637682793145`

Chris
ChrisT

Posts: 36
Joined: 16 October 2005

Thank you

I agree it's often easier to start over than to try and put things right when you've gone wrong, though somehow it seems slightly easier to make corrections on Killers than on ordinary Sudokus.
CathyW

Posts: 316
Joined: 20 June 2005

Just a quick note before I knock off work. The first one was a learning experience: I started with a particular "key" I wanted (in the lower right corner) then went from there. I'm not sure how professional puzzle-creators go about their business: you can basically approach things from two directions:

1. write out a grid of numbers, then draw boxes around them & pencil in the sums; this guarantees a soluble puzzle but I can't see how you could really finesse the solving process this way (i.e. control the entrypoints & strategies for solving it); & it wouldn't necessarily be easy to produce a unique solution. (This is to my knowledge the approach used by computerized puzzle-creators: randomly fill a grid with numbers then draw random cages around them.)

2. write out the particular combinations of cages you want, carefully "solving" the puzzle at each stage as far as possible, then adding more, until the puzzle is finished. The problem with this strategy is that, as I said, it's very hard to avoid creating impossibilities, though I found that the 2nd time around I had a lot better idea of how to avoid this. It helps if you photocopy the half-finished puzzle at key stages, before you do something that may wreck it.

I suspect that professional creators use a combination of both methods. The other thing is that it's a lot easier to create puzzles if you avoid "all-over-the-place" design: for instance, in my creation of #2, I worked out the middle row of nonets first, then worked out the bottom row, then worked out the top row. (Unless I've screwed up, I think this is probably the simplest way to approach solving it too, beginning with the middle nonet.) In other words I was avoiding working both the horizontal and vertical axes at the same time, which is a way to quickly get into contradictions. That said, that strategy does limit the "kind" of puzzle you can create so I want to work out ways of doing all-over-the-place design which are less error-prone.

26 minutes, eh? That's about what I'd hoped for. Chris's posted solution to #1 is correct. I should add that, while there may be other ways in to the puzzle, the one I'd begun with was a plus-minus variant of the 45 rule in the bottom right nonet (the sum of the 3 cages is 20 + 11 + 6 = 37, so the difference between innie & outie must be 45 - 37 = 8, leaving 1 and 9 as the only possibilities). There's a slightly fancier variant of this idea in the 2nd puzzle.

The last few postings raise an interesting topic: in what situations is it possible to fix an erroneous solution? Is there any strategy that's not dependent on backtracking? (i.e. remembering your immediately previous moves & undoing them). (Thought experiment: someone hands you an unsolved puzzle where someone has made a mistake. So you don't know its past solving history. Is there anything salvagable or do you just have to erase it & start over?) -- I suspect that the answer to my questions is "almost never", & that knowledge of past history is necessary, but perhaps some of the more mathematically/computerly inclined might be able to give a firmer answer....
nd

Posts: 28
Joined: 11 September 2005

Just created a new one:

http://www.ndorward.com/blog/?p=67

Have fun--I tried to make it hard, though I'm sure that some of the hardcore solvers here will find it kid's play nonetheless.
nd

Posts: 28
Joined: 11 September 2005

Enjoyed it. Wouldn't call it kids play though !
afjt

Posts: 82
Joined: 07 September 2005

Heheheh... Glad to know it's not a pushover. -- Currently working on a 4th puzzle; I'm trying to make it require some types of solving strategies that are less basic (that I've learned from working on some of the harder Djape puzzles & from some of udosuk's comments).... will see if I can get it done sometimes this week.
nd

Posts: 28
Joined: 11 September 2005

Definitely not a pushover - I'm still working on it!!
CathyW

Posts: 316
Joined: 20 June 2005

Finished a 4th puzzle... but it's so hard that I'm having trouble solving it now! (I'm not satisfied that the logic I'd originally used to construct it is watertight, so I'm going back over it to make sure...) Once I assure myself that it is solvable without trial & error I'll post it up too.
nd

Posts: 28
Joined: 11 September 2005

OK, the 4th puzzle is ready:

http://www.ndorward.com/blog/?p=69

WARNING: this one is REALLY REALLY hard. Even after I created it I found it took a lot of work to solve.
nd

Posts: 28
Joined: 11 September 2005

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