Diagram

[cgrosinger]

Could some one please show me how they diagrammed this? for some reason my brain will not let me get this game digrammed properly!

Thanks!

[timmydoeslsat]

This is a classic 3D ordering game. We are ordering elements with three sets of information instead of the usual two along with the number line. We need to keep track of the airline name, whether it is D or I, and the name of the plane.

Here is my initial setup of the rules and diagram:



We know that there is a distinction made in the ordering of domestic flights, whereby G(D) is always ahead of the F(D)s. We also know that an I is ahead of the Ds. There is no distinction made between a G(I) and a F(I).

We know that we only have one F(D), this must be last.

We know that we must now maintain a P - R ordering. We also have two interchangeable flights of S and T. We know that they are both Gs. However, we do not know whether they are Ds or Is. So they are floaters at this point.

This is my diagram after those inferences:



Let me know if you have additional questions.

[tommywallach]

Hey Guys,

Great work here from timmydoeslsat. I can't improve on any of his diagrams, but I'll try to do a bit more explanation, in case some things don't quite make sense.



Here are the constraints diagrammed. A few notes on this. At first, you might be tempted to leave out the Fs and Gs, but as soon as you see that there's a constraint that relates to them (#6), you should realize it'll be helpful to include it in your diagram. I would put FFGGG, just to remind yourself of the number of F's and G's you should expect.

I also chose to write the last two constraints as negatives, rather than positives. The reason why I don't like writing constraint #5 as I -- D is that it says that I comes before D, but we don't technically know if there are any international flights at all. So I prefer to say that I should never see an international flight after a domestic. Similarly, I prefer to word the sixth constraint as a negative, because we do not HAVE to have a domestic flight for either Flyhigh or Getaway. But I do know that I should never see a domestic Flyhigh before a domestic Getaway.

These aren't major differences with timmy's take, but I like to give some variety, and show you what I'd actually do.

Let's move on to the inferences. Again, Timmy nailed them, but let's make sure we understand why:



The text is on the slides, but I'll repeat it here, with a bit more pizazz, just in case it's hard to read:

Inference #1: The international flight has to come before the domestic flights, and the Getaway domestic has to come before the Flyhigh domestic. This allows us to order the three flights that we have full information about.

Inference #2: These are our remaining flights. If either of them is domestic, that flight will have to come before the FDQ flight (the third one we have ordered), because of Constraint #6. If either of them are international, that flight would have to come before both GDR and FDQ, because of Constraint #5. This means that FDQ has to go in the final position, as nothing else can come before it.

Let me know if you have any further questions!

(Thanks, Timmy!)

-t