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- - **I see the solution, but what's the logic?**
(*http://www.logic-puzzles.org/forum/showthread.php?t=299*)

I see the solution, but what's the logic?2 Attachment(s)
Here's the blank:
Attachment 86 And here's the bottleneck: Attachment 87 If you replace mushroom with Fusilli, clues 1 and 5 reduce to just two categories: Yolanda plus $1 is Capellini Fusilli plus $1 is Angie With: Angie not Yolanda Fusilli not Capellini Angie not Capellini Yolanda not Capellini I worked it out that this cannot happen: Angie is $9.99 Fusilli is $8.99 Leaving Yolanda to be either: Yolanda is $7.99, but Capellini cannot be $8.99 (already taken) Yolanda is $8.99, but Capellini cannot be $9.99 (Angie cannot be Capellini) So, Angie must be $8.99, and she is, and everything falls into place. BUT WHAT IS THE LOGIC beyond the bottleneck? I don't see it. How do I frame what's left into a logical statement? |

Yikes, this one is tricky. Hopefully this will make sense.
Clue 5 - Angie is $1 more than the mushroom sauce. So either $7.99=mushroom/$8.99=Angie -OR- $8.99=mushroom/$9.99=Angie. So either way, $8.99 must be Angie or whoever had the mushroom sauce (either Wade or Yolanda), so you can eliminate Margie from $8.99. Therefore you can eliminate $8.99 from capellini After that, go back to clue 1 and you can now eliminate $7.99 from Yolanda So now, from clue 1 again, but substituting Margie for capellini: $8.99=Yolanda/$9.99=Margie or $9.99=Yolanda/$10.99=Margie. So $9.99 must be either Margie or Yolanda, which leaves Angie at $8.99 |

And here is yet another method using the two ordering clues with a substitution.
Lay out clues 1 and 5 with the substitution for capellini. Yolanda -> capellini = Margie mushroom -> Angie Notice that Margie and Angie are in the same category, same side of the relation, and a fixed distance from the left side. That means Yolanda cannot be mushroom. Wade must be mushroom. Shriekingviolet has a more interesting approach, and it demonstrates how the one-sided "Of A and B, one is C and the other is D" clue can yield extra Xs beside the obvious one. "A is either C or D" is very similar to its two-sided cousin. Just find out what C and D can never be, and apply those exclusions to A. As SV points out, from the partial solution grid, $8.99 is either Angie or mushroom. From the grid, we see that the intersection of Angie and mushroom also has four Xs that can be applied to $8.99. One of these Xs is "$8.99 cannot be Margie." |

Thanks to ShriekingViolet and Zenobia43 for laying this out. Yet another technique learned, here.
I'm working up a graphic to explain it all for anyone who doesn't see it. I'll link to it here in a few minutes. Zenobia43, it looks like I still need work on my approach to multiple fixed-relational clues that use the same category. That would have solved it for me. |

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