The New Sudoku Players' Forum

[markf]

and actually I see now that if r9c3 = 4 I can't draw any conclusion about r9c2. oops. Ah the sweet joy of being wrong on the sudoku forum. oh well I'll try to work it out from here or at least follow rubylips' explanation.

mark

[ronk]

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Consider the chain r3c7+<4|1>+r3c4~1~r9c4-2-r8c4-2-r8c7.
When the cell r8c7 contains the value 4, some other value must occupy the cell r3c7, which means that the value 2 must occupy the cell r8c7 - a contradiction.

Excellent elimination. However, your equation doesn't communicate the "When the cell r8c7 contains the value 4" unless it is prefixed with "r8c7~4~" resulting in ...

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Consider the chain r8c7~4~r3c7+<4|1>+r3c4~1~r9c4-2-r8c4-2-r8c7

[markf]

Thanks Rubylips,
By placing 2 in r8c7 then the clue provided by bennys earlier in the thread lets one place the 7 in r9c2, and then it unravels.

Can someone point me to a site where I can get explanation of the notation used in those explanations, ~ > etc? Just assume I don't have any logic training. Or is that a given? Anyway.

thanks in advance,
mark

[rubylips]

Can someone point me to a site where I can get explanation of the notation used in those explanations, ~ > etc?

Unfortunately, I make up most of this notation as I go along but don't bother to document it. Some time ago, wolfgang introduced '-' for a strong link (i.e. two instances of a value within a sector) and '~' for a weak link (more than two instances). Since then I've introduced '=' for an extended link (see Strong Nice Loop: a new concept) and '+<v1|v2>+' for a disjoint subset link (though the '+' will soon be replaced by a '-') plus some more obscure link types that are hardly ever seen. The link r3c7-<4|1>-r3c4 should be read When r3c7 doesn't contain a 4, r3c4 must contain a 1. The justification for the link, as mentioned earlier in the thread, is that when r3c7 doesn't contain a 4, a disjoint subset is set up in Row 3 that forces r3c4 to contain a 1.

[QBasicMac]

I never saw a triple.

Mac

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r8c23=25 thus erase 2 in r8c1 and r8c8 plus erase 5 from r8c1
3 is locked in r56c1 thus erase 3 from r13c1
r7c56=35 thus erase 5 from r7c1
r78c1 (two cells) contain all 48 in box 7 thus erase 2 from r7c1
r13c8 (two cells) contain all 79 in box 3 thus erase 13 from both.
1 is locked in r13c9 thus erase 1 from r45c9
r5c6 contains the only 1 on row 5 thus r5c6=1
The rest are singles


Mac

[QBasicMac]

x86 XX2 4XX
etc.

You helped me find a limitation in my scratch pad www.SuDoku.funURL.com.

Namely, it normally accepts puzzle descriptions in any format, but was surprised by your lower case "x" at the beginning. So it concluded "X" was the unsolved-cell character, but could not find enough of them and stopped with an error message reporting illegal input. Took a while before I noticed the "x". Program is fixed now to convert all input to upper case before analysis.

Thanks, mark!

Mac

[rubylips]

I never saw a triple.

The last few posts on this thread have discussed the puzzle markf posted at the top of the second page - not the puzzle that started the thread.

[ronk]

'+<v1|v2>+' for a disjoint subset link (though the '+' will soon be replaced by a '-')

I made a suggestion similar to that recently here, but now strongly believe such a change would be a step backwards.

I view '<v1|v2>' syntax as value 'grouping' syntax ... and the '-', '~', and '+' as operands, much like '+', '-', '*', and '/' are arithmetic operands. So let's review the (left-to-right only) implications of the three operands with examples:

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r1c1-3-r1c7: A strong link has two valid implications ...
  1a) If r1c1=3, then r1c7<>3
  1b) If r1c1<>3, then r1c7=3

r1c1~3~r1c7: A weak link has only one valid implication ...
  2) If r1c1=3, then r1c7<>3

r1c1+<3|5>+r1c7: An Almost Disjoint Set link has only one valid implication ...
  3) If r1c1<>3, then r1c7=5

Now 3) makes the Almost Disjoint Set link look like a strong link (which is what I thought when I wrote the post referenced above) but it has only one of the two implications of a strong link, so I now believe it should keep an operand symbol distinct from both the strong and weak links.

[markf]

Many thanks all.
mark

[QBasicMac]

The last few posts on this thread have discussed the puzzle posted at the top of the second page - not the puzzle that started the thread.

Oh. Never mind.

Mac

[rubylips]

r1c1+<3|5>+r1c7: An Almost Disjoint Set link has only one valid implication ...
3) If r1c1<>3, then r1c7=5

No, the link is symmetric, i.e. when r1c7<>5, r1c1=3, which means that '-' is probably more appropriate.

[ronk]

r1c1+<3|5>+r1c7: An Almost Disjoint Set link has only one valid implication ...
3) If r1c1<>3, then r1c7=5

No, the link is symmetric, i.e. when r1c7<>5, r1c1=3, which means that '-' is probably more appropriate.

That's a very weak (pun intended) argument. The weak link .. r1c1~3~r1c7 .. is also symmetric, and using your argument, the '-' is then probably more approprate there too.

It's not about symmetry, but about whether one can assign as implication operands only "equals", only "not equals", or either "equals" or "not equals" at a link end ... when beginning to "traverse" the link in either direction.

Now for the Almost Disjoint (Locked) Set link .. r1c1+<3|5>+r1c7 .. one can easily "see" the only "not equals" because of the '<3|5>', but I think that syntax should be associated with the value set ... not the assignable implication operand.