For those of you who are experiencing UR technique withdrawl, here's something to ponder.

Ron asked for an example of:

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`abc ab . | abY . . `

. . . | . . .

. abc . | ab . .

abc in the intersection of the AUR's abY row and the AUR's abc box

excludes 'a' and 'b' from abY

I'm having an even more fundamental problem. I've been trying to find an example of a type 5 UR and have failed. Thinking about it I've come to the conclusion that they should occur infrequently. My arguement is somewhat weak, but here goes. A type 5 looks like:

- Code: Select all
`ab abc`

abc ab

The key is the missing "c" from the top-left "ab" or equally the bottom-right "ab". If the "c" is missing then there must be something usually in its row, column, or box which eliminates it, but if the "c" is eliminated from something in its row then the "c" in the top-right "abc" will very likely be eliminated as well distroying the type 5; if by something in its column, then the "c" in the bottom-left "abc" will very likely be eliminated; and if by something in its box, then the "c" in which ever "abc" shares a box with the "ab". It is possble for a "c" to be eliminated, for example, a UR+4X/2SL can remove a "c" without affecting other UR cells. Even if the Type 5 UR exists, then there still must be a "c" in one of the 4 cells where eliminations can occur for the Type 5 to register in my solver. The closest I have come is what's been called a UR+3x where one only "c" is missing:

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`+-------------------+----------------+------------------+`

| 169 257 12569 | 679 3 4 | 1567 8 56 |

| 368 378 368 | 1 57 56 | 4 9 2 |

| 4 57 1569 | 679 8 2 | 1567 13 356 |

+-------------------+----------------+------------------+

| *138 -2348 7 | 5 24 *138 | 19 6 49 |

| 5 9 12 | 67 247 16 | 3 14 8 |

| *138 6 148 | 48 9 *13 | 2 5 7 |

+-------------------+----------------+------------------+

| 3689 358 35689 | 2 1 7 | 569 34 34569 |

| 2 45 459 | 3 6 59 | 8 7 1 |

| 7 1 369 | 48 45 589 | 569 2 3569 |

+-------------------+----------------+------------------+

Also, believe it or not, we missed one more UR elimination. It fits between Keith's ALS technique and the strong link techniques:

UR+4/1SL: four UR cells with extra candidates, plus one strong link and at least two extra cells

--- UR+4x/1SL: "Y" and "Z" are single candidates "y" and "z", the extra cell "(ab)y" can contain "a" if it shares a house with "abW" and/or "b" if it shares a house with "abX", similarly the extra cell "(ab)z" can contain "a" if it shares a house with "abW" and/or "b" if it shares a house with "abX" => "b" can be removed from "abX".

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`abW-----abX `

a

aby abz (ab)y (ab)z

--- UR+4X/1SL: includes the extra cell(s) "(ab)U..." such that "U" is a locked set which includes "Y", "abY" is seen by all of the cells of "(ab)U..." which contain elements of "Y", and "(ab)U..." can contain "a" if all of its cells which contain "a" are seen by "abW" and/or can contain "b" if all of its cells which contain "b" are seen by "abX" and similarly for "(ab)V..." where "V" is a locked set which includes "Z" => "b" can be removed from "abX".

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`abW-----abX `

a

abY abZ (ab)U... (ab)V...

For Example:

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`+---------------+---------------+----------------+`

| 5 1 2 | 3 8 7 | 49 49 6 |

| 3 7 4 | 9 6 5 | 8 12 12 |

| 68 68 9 | 1 2 4 | 3 5 7 |

+---------------+---------------+----------------+

| 489 3 16 | 46 7 @89 | 2 149 5 |

| 2 489 7 | 5 -149 *189 | 6 3 149 |

| 49 5 16 | 2 3 16 | 49 7 8 |

+---------------+---------------+----------------+

| 469 469 5 | 7 #49 2 | 1 8 3 |

| 7 2 3 | 8 *149 *169 | 5 469 49 |

| 1 49 8 | #46 5 3 | 7 2469 249 |

+---------------+---------------+----------------+

UR+4X/1SL: r58c56, ALS1=r9c4|r7c5, ALS2=r4c6, r5c5=1=r8c5, => r5c5<>9

I've updated the list of techniques.