## Pivotal Cell and Three Strong Links

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

### Pivotal Cell and Three Strong Links

This puzzle is from Ruud via tarek.

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`048003006000500000020086007300000000056070120000000004200360010000009000900200430<`

It contains a pivotal cell and three strong links: [r5c1]=4=([r4c3],[r5c6],[r8c1])

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`# Multi-Colors easily confirms that the pivotal cell must be <4>.# pivotal cell         Blue  [r5c1]               = 4 or else ...# linked  cells        Green [r4c3],[r5c6],[r8c1] = 4# linked  cells = 4 => Pink/Amber          [r7c36]<>4 => contradiction! *--------------------------------------------------------------------* | 157    4      8      | 17     129    3      | 259    59     6      | | 6      379    379    | 5      249    247    | 2389   489    1      | | 15     2      1359   | 14     8      6      | 359    459    7      | |----------------------+----------------------+----------------------| | 3      1789  -12479G | 1468   1245   12458  | 56789  56789  589    | | 48B    5      6      | 9      7     -48G    | 1      2      3      | | 178    1789   1279   | 168    3      1258   | 56789  56789  4      | |----------------------+----------------------+----------------------| | 2      78     457P   | 3      6      4578A  | 5789   1      589    | |-14578G 1378   13457  | 1478   145    9      | 5678   5678   2      | | 9      6      157    | 2      15     1578   | 4      3      58     | *--------------------------------------------------------------------*`

As I recall, the few examples that I've encountered have the pivotal cell being true. Does anyone have an example where the pivotal cell is false?

===== ===== ===== ===== Addendum

Assuming Pivotal Cell (@) is false and Linked Cells (+) are true in the above puzzle:

Candidates are eliminated from (-) cells and must exist in a limited environment in the remaining units. Upon close examination, the puzzle above fails to have the candidate in any of the acceptable cells (.) in [b8] or [r7].

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`*-----------------------------*| -  .  - | .  .  - | .  .  . || -  .  - | .  .  - | .  .  . || -  .  - | .  .  - | .  .  . ||---------+---------+---------|| -  -  + | -  -  - | -  -  - || @  -  - | -  -  + | -  -  - || -  -  - | -  -  - | .  .  . ||---------+---------+---------|| -  -  - | .  .  - | .  .  . || +  -  - | -  -  - | -  -  - || -  -  - | .  .  - | .  .  . |*-----------------------------*`
Last edited by daj95376 on Mon Nov 06, 2006 9:07 pm, edited 1 time in total.
daj95376
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Posts: 2624
Joined: 15 May 2006

daj95376 wrote:As I recall, the few examples that I've encountered have the pivotal cell being true. Does anyone have an example where the pivotal cell is false?

A candidate that is part in three strong links, but doesn't appear in the solution? Lots of examples, for example take any grid with three unsolved instances of a digit, where none of the remaining candidates are hidden singles:
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` X  X  .  | .  .  .  | .  .  .  | ---------+*X  .  .  | X .  .  .  | . . #X  .  | X`

RW
RW
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Joined: 16 March 2006