## Solution to "Set reduction"

Advanced methods and approaches for solving Sudoku puzzles

### Solution to "Set reduction"

I am new to Sudoku. I normally try to solve one of the Savant Registered daily puzzles> often come against what they term "Set reduction" which is defined or described as:"The total number candidates in a group of cells exactly matches the number of cells containing them."

What I cannot figure out is which of the involved candidates should be crossed off.

Can anyone help, please. If so, use "click by click" basic language.

clivem.
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clivem

Posts: 3
Joined: 05 July 2008

### Re: Solution to "Set reduction"

clivem wrote:"The total number candidates in a group of cells exactly matches the number of cells containing them."

What I cannot figure out is which of the involved candidates should be crossed off.

In most places that's known as naked pairs, naked triples and naked quads ... and naked n-tuples or naked sets, in general. Angus Johnson's step-by-step guide should help.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

clivem wrote:---often come against what they term "Set reduction"
which is defined or described as
The total number candidates in a group of cells
exactly matches the number of cells containing them

What I cannot figure out is,
which of the involved candidates should be crossed off

when the "group of cells" is within one unit (a row, a column, or a box),
this "group of cells" will use up those candidates for that entire unit
-- so, remove those candidates elsewhere in that unit

Pat

Posts: 3879
Joined: 18 July 2005

In column 1 there is a naked pair on 67.
We have 2 cells and two candidates. "That uses up" all the 6s and 7s in that column.
Thus the 7s are not possible in r7c1 and r8c1.

Code: Select all
`.---------------------.| 2      7      68    || 9      4      68    || 5      3      1     |:---------------------+|#67     8      5     ||#67     1      279   || 3      29     4     |:---------------------+| 148-7  6      279   || 48-7   29     3     || 18     5      29    |'---------------------'`

In the middle box there is a naked pair on 67.
There can be no other 6 or 7 in that box, thus r5c3 cannot be 7.

Code: Select all
`.---------------------.| 2      7      68    || 9      4      68    || 5      3      1     |:---------------------+|#67     8      5     ||#67     1      29-7  || 3      29     4     |:---------------------+| 148    6      279   || 48     29     3     || 18     5      29    |'---------------------'`

It doesn't matter which order you do them in or whether you do them all "at once".

You could have looked at the last elimination differently, still valid, but it shows a slightly different type of elimination.

In the middle box only cells r5c3 and r6c2 have the digits 29.
That is a hidden pair and since we have 2 cells and 2 candidates there can be no other candidates in those 2 cells and we eliminate the 7 from r5c3

Code: Select all
`.---------------------.| 2      7      68    || 9      4      68    || 5      3      1     |:---------------------+| 67     8      5     || 67     1     #29-7  || 3     #29     4     |:---------------------+| 148    6      279   || 48     29     3     || 18     5      29    |'---------------------'`

Edited to correct typos, thanks clivem!
Last edited by wintder on Sat Jul 12, 2008 11:02 am, edited 2 times in total.
wintder

Posts: 297
Joined: 24 April 2007

Thank you ronk, thank you Pat and thank you wintder. It is very helpful to know that one can get the solutions to my problem by looking at the involed numbers as naked pairs etc., something that I can understand.

wintder rote "In the middle box there is a naked pair on 67.
There can be no other 6 or 7 in that box, thus r3c5 cannot be 7." I think it should read "r5c3' but not "r3c5" Or is it a deliberate mistake for a novice like I?!

Pat's suggestion will probably to a quicker solution but I will have to think it out carefully before I can understand it fully and absorb it.

Angus Johnson's step-by-step guide is fine. It is now among my Favourites for future references.

Thanks again,

clivem.
clivem

Posts: 3
Joined: 05 July 2008

### re(2): "naked" subset

clivem wrote:Pat's suggestion will probably to a quicker solution
but I will have to think it out carefully before I can understand it fully and absorb it.

hi clivem,

i wasn't making a separate suggestion,
merely explaining the logic of the "naked" subset
and i thought it would be good to give the proper definition of the "naked" subset
i.e. add that the "group of cells" must be within one unit

Pat

Posts: 3879
Joined: 18 July 2005

Hi Pat,