The New Sudoku Players' Forum

[SuDokuKid]

I have 278,268,268.

Can I make that 28,268,268?

[PaulIQ164]

Only if there aren't any 2s or 6s or 8s anywhere else in the row (or column or box or whatever it is).

[SuDokuKid]

Only if there aren't any 2s or 6s or 8s anywhere else in the row (or column or box or whatever it is).

Perfect! THX

[tso]

I have 278,268,268.

Can I make that 28,268,268?

No. There is no triple of any kind. You have three cells with FOUR values. A triple requires exactly three values in exactly three cells.

For example, if your situation were ...

Code: Select all

[278][268][268]|   1    3    4   |   5    9    ?


... no elimination could be made, as all of the following would be possible solutions:

Code: Select all

[2  ][ 6 ][  8]|   1    3    4   |   5    9    ?
[2  ][  8][ 6 ]|   1    3    4   |   5    9    ?
[ 7 ][2  ][ 6 ]|   1    3    4   |   5    9    ?
[ 7 ][2  ][  8]|   1    3    4   |   5    9    ?
[ 7 ][ 6 ][2  ]|   1    3    4   |   5    9    ?
[ 7 ][ 6 ][  8]|   1    3    4   |   5    9    ?
[ 7 ][  8][2  ]|   1    3    4   |   5    9    ?
[ 7 ][  8][ 6 ]|   1    3    4   |   5    9    ?
[  8][2  ][ 6 ]|   1    3    4   |   5    9    ?
[  8][ 6 ][2  ]|   1    3    4   |   5    9    ?


As you can see, each cell still has three possible values.

[SuDokuKid]

Now I'm confused. What is the difference between the above and something like this:

Cleaning up chains:

If a chain exists, then all additional possibilities in the chain can be discarded.
Chains of 2 numbers require 2 cells, chains of 3 numbers 3 cells and so on.
Example:
{4, 5, 6, 9}, {4, 9}, {5, 6, 9}, {2, 4}, {1, 2, 3, 4, 7}, {1, 2, 3, 7}, {2, 5, 6}, {1, 2, 7}, {8}

This group has a 3-number chain for the numbers (1, 3, 7): {1, 2, 3, 4, 7}, {1, 2, 3, 7}, {1, 2, 7}. Clearly the three numbers can only be in these three cells and no other numbers are possible. We can therefore simplify those cells to read: {1, 3, 7}, {1, 3, 7}, {1, 7}.

I have 278,268,268.

[emm]

We don't know what the other numbers in the row are - perhaps it might help to post them.

Say they were -

Code: Select all

278    268    268  |   13    37    47   |   57    97    17

then yes you can exclude the 7 in c1 as there are no other 2, 6, 8 in the group.

Hidden triple - "if three candidates are restricted to three cells in a given group, then all other candidates in those three cells can be excluded." SS

[tso]

Now I'm confused. What is the difference between the above and something like this:

Cleaning up chains:

If a chain exists, then all additional possibilities in the chain can be discarded.
Chains of 2 numbers require 2 cells, chains of 3 numbers 3 cells and so on.
Example:
{4, 5, 6, 9}, {4, 9}, {5, 6, 9}, {2, 4}, {1, 2, 3, 4, 7}, {1, 2, 3, 7}, {2, 5, 6}, {1, 2, 7}, {8}

This group has a 3-number chain for the numbers (1, 3, 7): {1, 2, 3, 4, 7}, {1, 2, 3, 7}, {1, 2, 7}. Clearly the three numbers can only be in these three cells and no other numbers are possible. We can therefore simplify those cells to read: {1, 3, 7}, {1, 3, 7}, {1, 7}.

I have 278,268,268.

In this example, you have a "hidden triple". The digits 1, 3 and 7 appear in exactly three cells, therefore, one of each MUST be in in each of these cells. All candidates other than 1, 3 and 7 may be eliminated from those three cells.

Look at it this way -- in a single row, column or box, if ONE digit can only appear in ONE cell, you can eliminate all other candidates from that cell (and write fill in the digit). This is a hidden single.

If TWO digits can only appear in TWO cells, you can eliminate all other candidates from those two cells. This is a hidden pair.

If X digits can only appear in X cells, you can eliminate all other candidates from those X cells.

In each case, the contents of ALL NINE CELLS in the row, column or block are needed to make a logical deduction. "I have 278,268,268" doesn't give enough information. If none of the other six cells contain a 2, 6 or 8 -- then the 7 in the first cell can be eliminated. One the other hand, if none of the other six cells contain a 7, then the first cell MUST BE a 7. You simply haven't given enough information to make any logical deduction.

Given this row ...

Code: Select all

[278][268][268]|   1    3    4   |   5    9    [123678]


... no deduction can be made.


Given this one:

Code: Select all

[278][268][268]|   1    3    4   |   5    9    [12368]


... the only place for a 7 is the first cell.



Finally:

Code: Select all

[278][268][268]|   1    3    4   |   5    9    [137]


... the only places for 2, 6 or 8 is in cells 1, 2 and 3 --- and in this case, the 7 can in the first cell can be eliminated.