## Overlapping sudoku

Post the puzzle or solving technique that's causing you trouble and someone will help

### Overlapping sudoku

I got this from the times online some time ago. There is four 9x9 that partly overlap eachother.
Additionally, the diagonal lines on all four sudokus shall have the numbers 1-9.

xxx xxx xxx xxx
2xx xxx xxx xx9
xxx 9x8 2x5 xxx
xxx xxx xxx xxx
xxx x5x x6x xxx
xxx 68x x32 xxx
xxx 19x x86 xxx
xxx x2x x4x xxx
xxx xxx xxx xxx
xxx 3x2 8x4 xxx
2xx xxx xxx xx8
xxx xxx xxx xxx

I am stuck. Can anybody help?
bjnorse

Posts: 3
Joined: 09 April 2006

Hi bjnorse

I really like these overlapping puzzles. This is how I attack them.

First, split it into 4 separate 9x9 sudokus:

Code: Select all
`. . .|. . .|. . .2 . .|. . .|. . .. . .|9 . 8|2 . 5-----+-----+-----. . .|. . .|. . .. . .|. 5 .|. 6 .. . .|6 8 .|. 3 2-----+-----+-----. . .|1 9 .|. 8 6. . .|. 2 .|. 4 .. . .|. . .|. . .. . .|. . .|. . .. . .|. . .|. . 99 . 8|2 . 5|. . .-----+-----+-----. . .|. . .|. . .. 5 .|. 6 .|. . .6 8 .|. 3 2|. . .-----+-----+-----1 9 .|. 8 6|. . .. 2 .|. 4 .|. . .. . .|. . .|. . .. . .|. . .|. . .. . .|. 5 .|. 6 .. . .|6 8 .|. 3 2-----+-----+-----. . .|1 9 .|. 8 6. . .|. 2 .|. 4 .. . .|. . .|. . .-----+-----+-----. . .|3 . 2|8 . 42 . .|. . .|. . .. . .|. . .|. . .. . .|. . .|. . .. 5 .|. 6 .|. . .6 8 .|. 3 2|. . .-----+-----+-----1 9 .|. 8 6|. . .. 2 .|. 4 .|. . .. . .|. . .|. . .-----+-----+-----3 . 2|8 . 4|. . .. . .|. . .|. . 8. . .|. . .|. . .`

The second puzzle can be advanced with 2 hidden single 2 in R9C5. Place this single, but you can also place it in the same (relative) position in the 3 other puzzles. You will see that placing the 2 in the 3rd puzzle will create another hidden single in R9C7. This one can only be transferred to puzzle 4.

At some point you will need the diagonals. Just keep an eye on the number of candidates for each digit in the diagonals, and eliminate candidates when a digit is already placed in a diagonal.

Good luck.

Ruud.

I just found that the \ diagonal of component puzzle 4 does not have a location for digit 8. This means that either the puzzle is invalid or you have made an error in your transcription.

[End edit]
Ruud

Posts: 664
Joined: 28 October 2005

Thanks for the tip.
My transcript was wrong. It should be 9 in R8C9 of puzzle 4.
bjnorse

Posts: 3
Joined: 09 April 2006

There are 2 ways of attacking overlapping (merging) puzzles.....
you have to seperate them into individul puzzles......

1. start in one puzzle reaching a certain technique & not beyond that (box-line interaction), then move through the puzzles using the same threshold...........Most of them are solved this way....
if you go through all puzzles without advancing any, increase the threshold (let's say to naked triples)..........& so on

2.the second way is to gove every puzzle the best you got until you reach the dead end....(longer but probably more interesting for some)...& then go through the rest....and then start again

tarek

tarek

Posts: 2650
Joined: 05 January 2006

These butterflies have a feature that may help you solve it a little faster.

The digit in the boxes at the opposing borders (left+right, but also top+bottom) are connected. They must go in the same row (left+right) or column (top+bottom). So when you have eliminated all candidates in the intersection of a row/column and the border-box you can also eliminate all candidates of the opposing border box that intersect with the same row/column.

(I don't know if anyone understands this. It's not easy to explain)

Ruud.
Ruud

Posts: 664
Joined: 28 October 2005

I'm really surprised that I see this puzzle here.

As far as I know, this concept was first suggested by udosuk and first puzzles with this concept were created by me. Or at least that's what I thought. But if you are saying that you found this puzzle elsewhere, it's a big surprise for me.

udosuk called these puzzles "butterfly sudoku". I posted a few of those, both with diagonals and without them.

This particular puzzle that you copied is not a very nice "butterfly". I say this because these are solved using a technique called "twin nonets". Well, for this puzzle, those twin nonets are pretty much "identical twins" so to speak. Otherwise, with your correction that R8C9=9 and not 8, this puzzle is a valid butterfly.
djape

Posts: 34
Joined: 27 September 2005