The New Sudoku Players' Forum

by **rliu** » Sat Oct 28, 2006 5:46 am

Can anyone give me hints on this one, please?

Code: Select all: 157 3 8 | 4 9 6 | 257 1257 1257 9 2 6 | 1 5 7 | 4 3 8 157 157 4 | 2 8 3 | 6 1579 1579 --------------------+----------------------+-------------------- 3 6 7 | 9 1 4 | 258 258 25 45 45 1 | 8 6 2 | 3 79 79 8 9 2 | 7 3 5 | 1 4 6 --------------------+----------------------+-------------------- 124 14 5 | 6 7 9 | 28 128 3 67 8 3 | 5 2 1 | 9 67 4 1267 17 9 | 3 4 8 | 257 12567 1257

by **daj95376** » Sat Oct 28, 2006 6:22 am

Your puzzle has 17 solutions. Either the original puzzle wasn't unique, or else you made an error reducing it to this point. It's always advisable to post the original puzzle along with the PM.

by **rliu** » Sat Oct 28, 2006 9:38 am

Thanks for the reply. I just figured it out the original puzzle has more than 1 solutions. The puzzle didn't say that

However, I used it to test a new technique I just learnt so that I can reduce it further as follows:

Code: Select all: 15 3 8 | 4 9 6 | 257 25 1257 9 2 6 | 1 5 7 | 4 3 8 15 7 4 | 2 8 3 | 6 9 15 -------+-------+------------ 3 6 7 | 9 1 4 | 25 8 25 4 5 1 | 8 6 2 | 3 7 9 8 9 2 | 7 3 5 | 1 4 6 -------+-------+------------ 2 4 5 | 6 7 9 | 8 1 3 7 8 3 | 5 2 1 | 9 6 4 6 1 9 | 3 4 8 | 257 25 257

The original puzzle is:

Code: Select all: . . . | . 9 6 | . . . 9 . . | 1 5 7 | 4 3 . . . . | . 8 . | 6 . . -------+-------+------ . 6 7 | . . . | . . . . . 1 | 8 6 2 | 3 . . . . . | . . . | 1 4 . -------+-------+------ . . 5 | . 7 . | . . . . 8 3 | 5 2 1 | . . 4 . . . | 3 4 . | . . .

by **ravel** » Sat Oct 28, 2006 8:21 pm

rliu wrote:However, I used it to test a new technique I just learnt so that I can reduce it further as follows ...

Thats interesting now, i only can see 8 solutions in this grid, and also after common uniqueness eliminations, which might reduce the number of solutions, i cannot arrive at it.
Can you tell us more about the new technique ?

by **rliu** » Sun Oct 29, 2006 8:23 am

Can you tell us more about the new technique ?

After reviewing, I found a mistake. Sorry.

I can only eliminate a few more candidates but cannot reducing it further.

The technique is called Alternating Inference Chains.

Here is the original one I posted with labels A to F added:

Code: Select all: 157 3 8 | 4 9 6 | 257F 1257E 1257E 9 2 6 | 1 5 7 | 4 3 8 157 157 4 | 2 8 3 | 6 1579E 1579E --------------------+----------------------+-------------------- 3 6 7 | 9 1 4 | 258 258 25 45 45 1 | 8 6 2 | 3 79C 79D 8 9 2 | 7 3 5 | 1 4 6 --------------------+----------------------+-------------------- 124 14 5 | 6 7 9 | 28 128 3 67A 8 3 | 5 2 1 | 9 67B 4 1267 17 9 | 3 4 8 | 257 12567 1257

A7=B7-C7=D7-E7=F7

This means either r8c1 or r1c7 is 7. So, r1c1 cannot be 7. And, because of this, both r3c8 and r3c9 cannot be 7. The puzzle becomes:

Code: Select all: 15 3 8 | 4 9 6 | 257 1257 1257 9 2 6 | 1 5 7 | 4 3 8 157 157 4 | 2 8 3 | 6 159 159 --------------------+----------------------+-------------------- 3 6 7 | 9 1 4 | 258 258 25 45 45 1 | 8 6 2 | 3 79 79 8 9 2 | 7 3 5 | 1 4 6 --------------------+----------------------+-------------------- 124 14 5 | 6 7 9 | 28 128 3 67 8 3 | 5 2 1 | 9 67 4 1267 17 9 | 3 4 8 | 257 12567 1257

I have verified this.

by **Bluegoddess** » Thu Nov 02, 2006 7:10 pm

I'm a new lover of Sudoku, and I signed up for this forum because I saw your request for help with this puzzle. I copied and pasted it into Word and attempted a try. I think I may have got it. (I hope, that would be cool) I'm wondering if you have already completed the puzzle! I hope my answers are correct otherwise I'll look like an idiot!!

1 3 8 | 4 9 6 | 5 2 7
9 2 6 | 1 5 7 | 4 3 8
5 7 4 | 2 8 3 | 6 9 1
-------+-------+------
3 6 7 | 9 1 4 | 2 8 5
4 5 1 | 8 6 2 | 3 7 9
8 9 2 | 7 3 5 | 1 4 6
-------+-------+------
2 4 5 | 6 7 9 | 8 1 3
7 8 3 | 5 2 1 | 9 6 4
6 1 9 | 3 4 8 | 7 5 2

The New Sudoku Players' Forum

I was stuck. Please help.

I was stuck. Please help.

I think I might have the answer....