View Full Version : I see the solution, but what's the logic?
06-17-2013, 08:34 PM
Here's the blank:
And here's the bottleneck:
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
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?
06-17-2013, 09:30 PM
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
06-18-2013, 12:57 AM
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."
06-18-2013, 03:52 PM
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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