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.

Examine your suggestion again:

- 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.