## Question - Is this a "Hidden Triple"?

Everything about Sudoku that doesn't fit in one of the other sections

### Question - Is this a "Hidden Triple"?

Hi,

I wrote a bit of logic in my solver to identify Hidden Triples and it says that the following is one.

68, 479, 179, 2579, 1579, 12579, 127, 46789

It claims a triple 468 in 68, 479 & 46789.

Can anyone confirm this or if not suggest what it can be?

I personnally question the 479 component.

TIA,

louwin
louwin

Posts: 6
Joined: 11 July 2006

### "Hidden Triples" and Naked ....

louwin wrote:I wrote a bit of logic in my solver to identify Hidden Triples and it says that the following is one.

68, 479, 179, 2579, 1579, 12579, 127, 46789

It claims a triple 468 in 68, 479 & 46789.

Can anyone confirm this or if not suggest what it can be?

I personnally question the 479 component.

TIA,

louwin

There is a pair and a single, as 6 and 8 only appear in two cells in the row and after this reduction there is a single. since the second cell in your row has 4 7 and 9 in it, you can deduce that this cell must be a 4 (a Hidden Single).

You will notice that with a Hidden component (triple) comes a Naked component (quint-5), and you have five cells that only have 1 2 5 7 & 9 in them, so alternatively you can remove any of these numbers from the remaining cells in the row.

Last edited by Crazy Girl on Thu Jul 13, 2006 6:16 am, edited 1 time in total.
Crazy Girl

Posts: 189
Joined: 08 November 2005

Thanks for the confirmation.

I had been habouring under the misapprehension that a triple had to have at least two candidates of the triple so the 479 having only one candidate of the triple threw me.

I had just implemented the naked triple logic prior to this and will now proceed to the quad and quin techiniques.

Thanks again
louwin

Posts: 6
Joined: 11 July 2006

### Re: Question - Is this a "Hidden Triple"?

louwin wrote:Hi,

I wrote a bit of logic in my solver to identify Hidden Triples and it says that the following is one.

68, 479, 179, 2579, 1579, 12579, 127, 46789

It claims a triple 468 in 68, 479 & 46789.

Can anyone confirm this or if not suggest what it can be?

I personnally question the 479 component.

TIA,

louwin

I'm assuming that you only listed eight cells because the remaining cell has a single value. In any event, I don't think you have a Hidden Triple. What I see is a Hidden Pair in <68>. This then leaves a Hidden Single <4>.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Thanks.

I think you are right now that you mention it.

I couldn't quite reconcile 479 being part of the hidden triple.

I have to brush up on my code that should have detected the hidden pair.

Thanks again.

louwin
louwin

Posts: 6
Joined: 11 July 2006

louwin wrote:I have to brush up on my code that should have detected the hidden pair.

It doesn't seem likely that you ever need consider quints. You sure you want to code that?
fermat

Posts: 105
Joined: 29 March 2006

Like I said - I have done triples and am going to move on from that. After I fix my pairs detection logic.

Initially I was going to write discreet code to handle each technique, you know, a bit of code to do triples then quads then quins but I have now worked out a routine to do triples, quads, quins (and maybe sixes, whatever they are called) in one gigantic loop within a loop within a loop within a loop and so on.... Maybe I can encompass the pairs in the routine too.

I normally only do "Hard" sudokus while I vegitate in front of the TV but I thought I would try the current "Tough" one that casued this thread.

I only wrote the solver as an exercise to keep the programming skills from attrophying (sp?) while I look for another job. Company got taken over and I was made redundant.

It has been enjoyable talking to you all.

louwin
louwin

Posts: 6
Joined: 11 July 2006

In the Programmers Forum, I read a discussion explaining why n-tuples never need to go above testing for Quads. The logic goes ... once you reach the halfway point, then any n-tuple found is just the remnants of finding a smaller n-tuple in the other cells of the row/column/box.

(I hope that I paraphrased the discussion correctly!)
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Thanks for your comment. I can see the point of it but if coding for a 6-tuple solves just one puzzle then it is worth allowing for it.

Anyway entering

for tuple=3 to 6

is no real difference to

for tuple=3 to 4

In other words programming for quads or 6 (or even 7) tuple is just a matter of changing the "to" value in the program.

Thanks,

louwin
louwin

Posts: 6
Joined: 11 July 2006

Louwin,
If you have a 6-tuple in a row/column/box then the remaining cells must be one of the following:-
• 3 singles
• pair and single
• triple
And also if you have a 5-tuple in a row/column/box then the remaining cells must be one of the following:-
• 4 singles
• single and triple
• pair and two singles
• two pairs
So you could save time and computer usage by just looking for one of the above, and also make sure that you have locked candidates and X-Wing (and maybe XY-wing/colours if you want), then you will be able to solve 95-99% of published puzzles in newspapers and books.

The pappocom fiendish puzzles only require locked candidates, pairs and triples to solve them and possibly a X-wing at superior level.

Crazy Girl

Posts: 189
Joined: 08 November 2005

I've learnt more in the last couple of days than I did in the last month.

Like I said I am coding Hidden triples/quads/quins etc at the moment. I haven't got to X-Wing plus. Certainly NOT locked candidates etc. I just haven't got to those techniques as yet.

Thanks for all your input though.

Off to bed now - it is almost midnight in Perth, Western Australia.

louwin

Posts: 6
Joined: 11 July 2006

### hidden triple

I've been following the discussion on this question and now I am confused. I recognize that the post was a double and a single and I am not a programmer but now I am confused, basic principles, does all components of a triple have to have at least two of the elements. I didn't think that was the case, and would have seen the example as being a triple if it were not for the fact that it could be solved with a double and a single.

Posts: 8
Joined: 03 June 2006

Code: Select all
`[1] -- single[12][12] -- pair[12][1-] -- degenerate pair (includes single)[123][123][123] -- triple[123][123][12-] -- triple[123][1-3][12-] -- triple[-23][1-3][12-] -- triple[123][12-][12-] -- degenerate triple (includes pair)[123][123][1--] -- degenerate triple (includes single)`
tso

Posts: 798
Joined: 22 June 2005

louwin wrote:Thanks for your comment. I can see the point of it but if coding for a 6-tuple solves just one puzzle then it is worth allowing for it.

You will never find a 9x9 puzzle that needs a 6-tuple. If there is one it will be complemented bt a triple or pair.
You only have to code for hidden and naked sets up to quads
ab

Posts: 451
Joined: 06 September 2005