Diagram

[noah]

Here's a question that a student had that they posted in the wrong place, so I've moved it over here to it's rightful home:

Game 4 was unusually difficult for me. Can anyone show me how they diagrammed it?

[aileenann]

Thanks for your question! I am attaching my diagram in the form of a word document. Let me put in a few words of explanation, and feel free to follow up with me if you have any questions!


I thought of this game as a cross between a 3-d numbered ordering game (it's 3-d in a way, but not numbered) or as an assignment game (but where the things being assigned - type of furniture and type of wood are not interchangeable with one another). Basically, I needed a way to keep track of the fact that there are four slots to fill with one type of furniture (or in other words, one kind of furniture is excluded/not picked). If you wanted to be really thorough, you might even include a 5th slot as the "out" slot to designate the furniture that has not been picked, but this isn't necessary to do the problem unless you think you are likely to make the mistake of ignoring some conditions.


Speaking of catching things relating to excluding a type of furniture, there is one important secondary inference. There must always be a T. If there is an F, there must be a T selected. But if there is not an F, then F is the only piece of furniture excluded, and for that reason there must be a T selected again. This all hinges on the fact that only one of the five types of furniture is excluded from the list of Irene's purchases. However, we cannot write this T into the diagram because it may or may not be the piece of furniture that matches wood with another piece of furniture (designated as the two slots with X as the type of wood and distinguished from those with Y and Z types of wood.)


Another thing to notice, and that you could have noticed more directly (by not making the observation above), is that since we know it must always be either F or V that is excluded, it could be handy to make frames, since there will only be two. If V is excluded, then we know that F and T are the two pieces of furniture that are of the same kind of wood. I have not diagrammed out these two frames, but they certainly could be helpful!


Please post a reply if you have any specific questions about my diagram. I'd also love to hear if you have an alternate way to do it that you think works better.

[cdjmarmon]

I merely made my diagram like an In/Out game. I did 2 lines of 4 dashs (Top for wood and bottom for furniture) then made a vertical line and made another two level dash.

From there you can just add a T H S V/F. I saw those as the only possibilities becuase we can only have one piece of furniture out and its going to have to be V or F.

So everytime you do a problem you can just remake the 2 levels of 4 dash and start throwing the type of wood in there to quickly run through the problems.

[chike_eze]

I agree. This game is a hybrid -- 3d + in/out.

Key inference: Only V or F can be out. Why? Because if any other furniture is out, then that means V and T must be in... but that violates rule #3 V -> not F (F -> not V)

So: We end up with:

Code: Select All Code

F/V  |  F/V H S T
(out)


Which can be split into

Code: Select All Code

     m 
F  | V    H    S   T   

      m   o/p       m
V  |  F    H    S   T

      p   o/m       p
V  |  F    H    S   T


[ManhattanPrepLSAT1]

Nice work Chike! That's great!

[fowleramyfarah]

Amazing work!!! I am just flabbergasted by the diagrams..These are truly adorable and dynamic too..