## Triple confusion, 3rd try.

Advanced methods and approaches for solving Sudoku puzzles

### Triple confusion, 3rd try.

{5}{124}{1249}|{4789}{479}{2479}|{6789}{1678}{3}
The five and three at each end are solved.

wrong. Well not entirely (it’s true I don’t understand triples) but .....

The question was,"Can a triple be identified by inspection when
there is more than one possibility?
In row 1: the triple is col4-78, col7-678, col8-678, not the 479
combination."

The answer is yes you can if you are good at this game.

The 678 is a legitimate triple. The 479 is not a triple because you can’t have two 7’s in the same row.

Besides, the 2 in column 6 is a single, which like the dummy I am, I didn’t realize (and you didn’t mention), but when the 2 was solved it made the 49 double obvious and that made the 1 in column 2 a single.

Anyway, I couldn’t have figured all this heavy stuff out without the three references tso gave me. Thanks tso.
weesleekit2

Posts: 5
Joined: 04 October 2005

In row 1: the triple is col4-78, col7-678, col8-678, not the 479 combination. The 678 is a legitimate triple.

Actually, no. There is another 7 in row 1 - you can't have a triple with the candidates in 4 cells unless they are the ONLY candidates for three of the cells.

Hidden triple – the 3 candidates are in ONLY 3 cells in that row – ‘hidden’ because there are other candidates in those cells with them. Naked triple - three cells in the row contain ONLY these 3 candidates - 'naked' because well .... they are.

emm

Posts: 987
Joined: 02 July 2005

### Re: Triple confusion, 3rd try.

weesleekit2 wrote:...(it’s true I don’t understand triples) but .....

The question was,"Can a triple be identified by inspection

Difficult, but yes you can.

...when there is more than one possibility?

Then there is no triple.

In row 1: the triple is col4-78, col7-678, col8-678, not the 479
combination."

Wrong.

The answer is yes you can if you are good at this game.

i.e. triples.
Even then they can be difficult to spot.

The 678 is a legitimate triple. The 479 is not a triple because you can’t have two 7’s in the same row.

You could have said 'The 479 is a legitimate triple. The 678 is not a triple because you can’t have two 7’s in the same row.

Both of the above statements are wrong.

Besides, the 2 in column 6 is a single, which like the dummy I am, I didn’t realize (and you didn’t mention),

Yes I did.
In your second attempt I mentioned that there was a single number placement in box 2, although I did not say it was a 2, 2 was the only number that could be placed.

...but when the 2 was solved it made the 49 double obvious and that made the 1 in column 2 a single.

It's obvious that you do not understand doubles(pairs) either.
MCC

Posts: 1275
Joined: 08 June 2005

weesleekit2 wrote:{5}{124}{1249}|{4789}{479}{2479}|{6789}{1678}{3}
The five and three at each end are solved.

I) There are no triples, naked or hidden, in the row you've diagrammed.

II) A NAKED TRIPLE is exactly THREE CELLS, each of which has NO MORE THAN THREE CANDIDATES. All three cells share the SAME THREE CANDIDATES.

These four ARE naked triples:
Code: Select all
`a) [123][123][123]b) [123][123][12 ]c) [123][1 3][12 ]d) [ 23][1 3][12 ]`

This one, from your example above, is NOT a naked triple, as the cells have more than three candidates:

Code: Select all
`e) [4789][6789][1678]`

Examine (a) again:

Code: Select all
`a) [123][123][123]`

Here are the only six possible ways to fill these three cells:

Code: Select all
`[1][2][3][1][3][2][2][1][3][2][3][1][3][1][3][3][2][1]`

Each of these six results uses each of the digits 1, 2 and 3, eliminating them from the other 6 cells in the row.

Code: Select all
`e) [4789][6789][1678]`

You claim this is a 678 triple, but we can fill the cells:

Code: Select all
`[4][6][1][7][9][8]`

etc.

The fact that two of the cells contain 6 and all three contain 78 doesn't give us enough information for any conclusions.

III) A HIDDEN TRIPLE is THREE DIGITS that occur ONLY in THE SAME THREE CELLS and no where else in the row, column or box:

If you have this:
Code: Select all
`[12345][12367][12389][not 123][not 123][not 123][not 123][not 123][not 123]or[12345][12367][12 89][not 123][not 123][not 123][not 123][not 123][not 123]or[12345][1 367][12 89][not 123][not 123][not 123][not 123][not 123][not 123]or[ 2345][1 367][12 89][not 123][not 123][not 123][not 123][not 123][not 123]`

... the digits 1, 2 and 3 must be in the first three cells in some order, so you can remove the other candidates from those cells, leaving:

Code: Select all
`[123][123][123][not 123][not 123][not 123][not 123][not 123][not 123]or[123][123][12 ][not 123][not 123][not 123][not 123][not 123][not 123]or[123][1 3][12 ][not 123][not 123][not 123][not 123][not 123][not 123]or[ 23][1 3][12 ][not 123][not 123][not 123][not 123][not 123][not 123]`

... respectively.

IV) "Can a triple be identified by inspection when there is more than one possibility?"

I don't know what this could mean, but:

Code: Select all
`[123][123][123][456][456][456][any][any][any]`

... has two naked triples at once, and ...

Code: Select all
`[1239][1238][1237][4569][4568][4567][not 123456][not 123456][not 123456]`

... has two hidden triples, while ...

Code: Select all
`[1239][1238][1237][456][456][456][not 123][not 123][not 123]`

... has one of each.

weesleekit2 wrote:Anyway, I couldn’t have figured all this heavy stuff out without the three references tso gave me. Thanks tso.

Hey, don't blame me!

Ignoring candidates and pencil marks for the moment, say you have this situation:

Code: Select all
`1 2 3 | 4 5 6 | . . .. . . | . . . | . . .. . . | . . . | . . .`

Code: Select all
`1 2 3 | 4 5 6 | a a a. . . | . . . | x x x. . . | . . . | x x x`

You can see that the last three digits of the top row (marked 'a') must be 789 in some order, so the other 6 cells in the third box (marked 'x') CANNOT be 7, 8 or 9. This is a naked triple in action.

In this situation:

Code: Select all
`1 2 3 | . . . | . . . . . . | 1 2 3 | . . . . . . | . . . | x x x `

You can see that in the third box, the digits 1, 2 and 3 can ONLY be the three cells marked with an 'x' in some order. This is a hidden triple in action.
tso

Posts: 798
Joined: 22 June 2005

tso, there is some area of life that is missing you. I'm not sure what, but your skills are quite obviously not being appreciated.
Karyobin

Posts: 396
Joined: 18 June 2005

weesleekit2, I am a great fan of tso’s, even though he doesn’t know it and there are real gems in his posts, usually, but he’s a bit big for the little screen and sometimes after you’ve scrolled down 3 metres you can have lost the plot. What I do is print off his diktats and read them quietly on my own, when not distracted by other things and I have time to let it sink in. (mildly candid)
emm

Posts: 987
Joined: 02 July 2005