The New Sudoku Players' Forum

[m_b_metcalf]

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 . . 1 2 3 4 5 . .
 . . 6 . . . . . .
 . . 7 . . . . . .
 . . 3 . . . 4 . .
 . . 8 7 9 1 2 . .
 . . 9 . . . 1 . .
 . . 2 . . . . . .
 . . 4 . . . . . .
 . . 5 . . . . . .  easy

 . . 1 2 3 4 5 . .
 . . 6 . . . . . .
 . . 7 . . . . . .
 . . 3 . . . 4 . .
 . . 8 4 6 1 9 . .
 . . 2 . . . 1 . .
 . . 9 . . . . . .
 . . 4 . . . . . .
 . . 5 . . . . . .   hard


I try to ensure that the letters are sans-serif. This entails a step-by-step approach, and one such intermediate step for this letter came up with:

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 . . 1 2 3 4 5 . .
 . . 6 . . . . . .
 . . 7 . . . . . .
 . . 3 . . . 6 . .
 . . 5 8 4 2 7 . .
 . . 4 . . . 1 . .
 . . 2 . . . . . .
 . . 8 . . . . . .
 . 6 9 7 . . . . .   extremely hard

Mike

[Leren]

The Easy puzzle was the easiest so far, only basics. The Hard puzzle used some chains, and the Very Hard puzzle was indeed very hard - not much besides forcing chains.

To add some interest to this series, I suggest some discussion if something of interest may come up. So here is how far I got before chaining for the hard puzzle.

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*--------------------------------------------------------------------------------*
| 89      89      1        | 2       3       4        | 5       6       7        |
| 23      5       6        | 789     189     789      | 38      4       129      |
| 234     24      7        | 5689    1589    5689     | 38      29      129      |
|--------------------------+--------------------------+--------------------------|
| 6       1       3        | 89      2789    258      | 4       578     58       |
| 5       7       8        | 4       6       1        | 9       23      23       |
| 49      49      2        | 58      78      3        | 1       578     6        |
|--------------------------+--------------------------+--------------------------|
| 78      368     9        | 1       4       5678     | 2       358     358      |
| 278     238     4        | 356789  2589    56789    | 67      1       3589     |
| 1       2368    5        | 36789   289     26789    | 67      389     4        |
*--------------------------------------------------------------------------------*

Does SE (or Pat, or any one else for that matter) have some "magic" reasonably easy X based move that may make progress from here ?

Leren

[m_b_metcalf]

Leren,
From that point there is a SE=7.2 move. All details below.

HTH

Mike

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Analysis results
Difficulty rating: 7.3 (Forcing Chain)
This X Sudoku can be solved using the following logical methods:
43 x Hidden Single
1 x Naked Single
10 x Generalized Intersections
1 x Generalized Naked Pair
1 x Grouped Skyscraper 111
1 x Skyscraper 015
1 x Unique Rectangle type 4
1 x 3 Strong links 0016
1 x Grouped 4 Strong links 11052
1 x Bidirectional Y-Cycle
7 x Forcing Chain
The most difficult technique (ER): Forcing Chain

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Forcing Chain
If we assume that I8 contains the value 3, it follows, through a Forcing Chain, that I8 cannot contain the value 3. Therefore we can conclude that I8 does not contain the value 3.

The Forcing Chain consists of a chain of implications based on simple rules. The details of the Forcing Chain are given below.

Details of the Forcing Chain:
(1) If I8 contains the value 3, then B8 cannot contain the value 3 (the value can occur only once in the row)
(2) If B8 does not contain the value 3, then G3 must contain the value 3 (only remaining possible position in the Anti Diagonal)
(3) If G3 contains the value 3, then G2 cannot contain the value 3 (the value can occur only once in the block)
(4) If G2 does not contain the value 3, then A2 must contain the value 3 (only remaining possible position in the row)
(5) If A2 contains the value 3, then A2 cannot contain the value 2 (the cell can contain only one value)
(6) If A2 does not contain the value 2, then I2 must contain the value 2 (only remaining possible position in the row)
(7) If I2 contains the value 2, then I5 cannot contain the value 2 (the value can occur only once in the column)
(8) If I5 does not contain the value 2, then I5 must contain the value 3 (only remaining possible value in the cell)
(9) If I5 contains the value 3, then I8 cannot contain the value 3 (the value can occur only once in the column)

[Leren]

Hi Mike,

I put this puzzle through Andrew Stuart's Solver, and apart from a UR, he got to the same place I did before he started chaining. So nothing much of interest came up this time, but there is always next time.

Leren

[urhegyi]

Based on your extremely hard one but this time for the human p&p solver:

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..12345....6........7........3...6....58497....4...1....2........8.......693..... ED=4.2/1.2/1.2

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..12345..
..6......
..7......
..3...6..
..58497..
..4...1..
..2......
..8......
.693.....


[m_b_metcalf]

Based on your extremely hard one but this time for the human p&p solver:

Thanks. I'll give that a try.

M