The New Sudoku Players' Forum

[daj95376]

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 *-----------*
 |...|...|8..|
 |9..|.4.|.6.|
 |.2.|.68|..5|
 |---+---+---|
 |.3.|...|...|
 |.4.|.5.|...|
 |..6|...|798|
 |---+---+---|
 |..1|3.6|..4|
 |...|4..|.5.|
 |2..|57.|6..|
 *-----------* # gurth GC06


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# at this point:
# XY-Chain 3-[r2c7]-2-[r7c7]-9-[r8c7]-1-[r9c9]-3-[r9c8]-8-[r7c8]-2-[r5c8]-3-[r5c7]
 *-----------------------------------------------------------*
 | 4     6     5     | 1     2     3     | 8     7     9     |
 | 9     1     8     | 7     4     5     |a23    6     23    |
 | 3     2     7     | 9     6     8     | 4     1     5     |
 |-------------------+-------------------+-------------------|
 | 78    3     29    | 68    19    179   | 5     4     26    |
 | 78    4     29    | 68    5     79    | 12-3 g23    1236  |
 | 1     5     6     | 2     3     4     | 7     9     8     |
 |-------------------+-------------------+-------------------|
 | 5     7     1     | 3     89    6     |b29   f28    4     |
 | 6     89    3     | 4     189   2     |c19    5     7     |
 | 2     89    4     | 5     7     19    | 6    e38   d13    |
 *-----------------------------------------------------------*


However, steps (b)..(f) are simply a forced n-tuple relationship inside [b9]. Would it be acceptable to use

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XY-Chain 3-[r2c7]-2-[r7c7]..[r7c8]-2-[r5c8]-3-[r5c7]


as shorthand for this chain?

[Ocean]

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# at this point:
# XY-Chain 3-[r2c7]-2-[r7c7]-9-[r8c7]-1-[r9c9]-3-[r9c8]-8-[r7c8]-2-[r5c8]-3-[r5c7]
 *-----------------------------------------------------------*
 | 4     6     5     | 1     2     3     | 8     7     9     |
 | 9     1     8     | 7     4     5     |a23    6     23    |
 | 3     2     7     | 9     6     8     | 4     1     5     |
 |-------------------+-------------------+-------------------|
 | 78    3     29    | 68    19    179   | 5     4     26    |
 | 78    4     29    | 68    5     79    | 12-3 g23    1236  |
 | 1     5     6     | 2     3     4     | 7     9     8     |
 |-------------------+-------------------+-------------------|
 | 5     7     1     | 3     89    6     |b29   f28    4     |
 | 6     89    3     | 4     189   2     |c19    5     7     |
 | 2     89    4     | 5     7     19    | 6    e38   d13    |
 *-----------------------------------------------------------*


However, steps (b)..(f) are simply a forced n-tuple relationship inside [b9]. Would it be acceptable to use

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XY-Chain 3-[r2c7]-2-[r7c7]..[r7c8]-2-[r5c8]-3-[r5c7]


as shorthand for this chain?

You could write

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        3-[r2c7]-2-[r7c7]=2=[r7c8]-2-[r5c8]-3-[r5c7]   =>r5c7<>3


And there is also the shorter 'pure' xy-chain

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XY-Chain 3-[r2c7]-2-[r7c7]-9-[r8c7]-1-[r9c9]-3-[r2c9]

[ronk]

And there is also the shorter 'pure' xy-chain

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XY-Chain 3-[r2c7]-2-[r7c7]-9-[r8c7]-1-[r9c9]-3-[r2c9]

And the equally short 'pure' xy-chain

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r9c2-8-r9c8-3-r9c9-1-r8c7-9-r8c2-8-r9c2

[daj95376]

Thanks Ocean and ronk for the assistance!!!

Although I don't see how either of your examples for 'pure' XY-Chain results in [r5c7]<>3, I'll study them further. It may simply be that my understanding, of the definition in ScanRaid for XY-Chain, isn't up-to-date or correct.

Ocean: Aaaagh. Of course! My proposal was nothing more that trying to abbreviate an XY-Chain (as I know them) into a regular chain that's shorter. Your first example caused the to go on for me!