## A Pondering about killer Su Dokus

All about puzzles in newspapers, magazines, and books

### A Pondering about killer Su Dokus

I was wondering, if you take a finished Killer su Doku puzzle, and replace all the numbers like this:

1 --> 9
2 --> 8
3 --> 7
4 --> 6
5 --> 5
6 --> 4
7 --> 3
8 --> 2
9 --> 1

That is, replce every number x in the grid with (10-x), and then alter the totals of the cages accordingly (so a 14-cage that was 1-6-7 becomes a 16-cage that's 9-4-3), will you get an equivalent puzzle? Obviously, the puzzle will be valid (in the sense of having a correct solution), but will it be in essence the same puzzle, solveable by the same logical techniques at the same times in the same places? It seems to be that it would be, because the behaviour of groups of high numbers works the same way as groups of low numbers in the puzzle (like 24 has to be 9-8-7, so 6 has to be 1-2-3), but I can't work it out for sure. (Certainly it'd put paid to The Times' "Top Tip" to start with the smallest totals, seeing as in this equivalent puzzle they'd be the highest totals.)

What I'm essentially asking is this: In a regular sudoku puzzle, you can replace the numbers any way you like (swapping all the 3s and 4s, or whatever) and get the exact same puzzle to all intents and purposes. Obviously you can't do the same with Killers (or can you? Surely not) but, if you use the specific rearrangement above, does it then work?
PaulIQ164

Posts: 533
Joined: 16 July 2005

You obviously can't do the same with killers, but your suggestion of swapping x for 10-x in cells and y for 10*z-y where z is the number of cells in a given cage and y is the total of the cage would work fine.
Enigma

Posts: 53
Joined: 14 June 2005

Can't see the slightest problem with that there Paul. Maybe we should tell The Times that their 'Top Tip' should really read 'Start with the extreme values'?
Karyobin

Posts: 396
Joined: 18 June 2005

Paul, one way to see if it works with killer is to take a completed killer and exchange the numbers per your list.
MCC

Posts: 1275
Joined: 08 June 2005

That's certainly true. I've done it to one of the recent ones (Wednesday's, I think) if anyone wants to try it. Here:

PaulIQ164

Posts: 533
Joined: 16 July 2005

Karyobin wrote:Can't see the slightest problem with that there Paul. Maybe we should tell The Times that their 'Top Tip' should really read 'Start with the extreme values'?

I agree, the following cages have only one way of being completed

size - Value - Solution
2 - 3 - 1,2
2 - 4 - 1,3
2 - 16 - 7,9
2 - 17 - 8,9
3 - 6 - 1,2,3
3 - 7 - 1,2,4
3 - 24 - 7,8,9
3 - 23 - 6,8,9
4 - 10 - 1,2,3,4
4 - 11 - 1,2,3,5
4 - 30 - 6,7,8,9
4 - 29 - 5,7,8,9

and also some larger areas although these aren't as common
Pi

Posts: 389
Joined: 27 May 2005

PaulIQ164,

Hope there's nobody (except me) who took the troubles to attempt your remade puzzle... otherwise they'd have (painfully) come to the conclusion that it's unsolvable... before they realised that you've made mistakes in 2 of the cages inside the bottom right box.

Oh... and after rectifying those errors and solve the puzzle again, I could safely say that it's essentially the same as the original version, requiring no extra tricks and techniques at all... so you're not getting anything too interesting by performing those replacements...
udosuk

Posts: 2698
Joined: 17 July 2005

Oops.
PaulIQ164

Posts: 533
Joined: 16 July 2005