Binary Grouping and the Logic Chain

[ms08g]

I just started to apply your logic chain method to in/out and distribution grouping games, but I ran into a small problem:

It seems to me that for certain games (for example, PT 23, G2, where you have employees not-interviewed, interviewed, and hired) that there is an issue with using the logic chain. In this situation do you recommend just going with conditional logic statements, or do you connect multiple chains, use subscripts?

[bbirdwell]

That's a great question, and any of those potential answers could work. The game in question is the only game I can remember that has two distinct binary groupings, though there may be others that are escaping me at the moment. The bottom line is that the Logic Chain, like any other method for notating constraints, is a tool. Use it when it when it works, innovate and improvise with it when it doesn't seem to quite fit.

The logic chain is a great visual representation of the conditional statements - if they appear scant or incomplete or disconnected, you can always fall back on listing them out as a backup.

I've attached one possible diagram for the game you mentioned, where I made a chain with only the elements involved, making the top half of the chain "Interviewed" and the bottom half "Hired."

I just wrote out the last complex constraint beside the diagram rather than trying to include it in the diagram.

[velvet]

After learning Manhattan's logic chain method, I've been practicing doing binary/in-out games for a little bit. While most of the time the logic chain is invaluable, I firmly believe there are some games that do not deserve a logic chain. The notorious "CD" game of PT31 is a prime example of the latter, and I recently tried out the "Electrical appliance" game of PT48. As with the CD game, this logic chain is TOO time-consuming and in the end not effective in answering the questions compared to solely writing out the conditionals and contrapositives.
So what I want to know is whether there is way to know for certain when to utilize the logic chain or not? I noticed that for these 2 games the logic chain is "messy," but I don't think this is a clear enough criteria to evaluate using the chain or not.
Thanks in advance.

[noah]

Thanks for the question. In my opinion, there are three categories of binary games:

1. Games for which the chain destroys it.

2. Games for which the chain is simply a method of noting the rules (there are no "pinball connections").

3. Games for which it's easier to note the rules in another manner.

The first category is the most common, so it's great to be ready to kill those games.

The second category isn't problematic - you have to note the rules somehow, and if you know the chain method, you'll be able to quickly read the diagram. For me, having an in and out side is a lot faster than reading negative signs.

Finally, there are very few games that fall in the last category. So, you don't have to worry - particularly since it's not too hard to write down the rules of a game and follow them if you're in a pinch. These rogue binary grouping games fall into two categories, and those categories have pretty clear signals.

One would be if every rule is a compound conditional (like the CD game). Though you can solve it using the chain - note Dan's solution though many might simply choose to write out the rules for that one. Another would be if there are very few conditional rules based on elements and mostly they're based on numerical issues. Then you'd probably want to focus on what are possible numerical frames.

By the way, I think the appliance game is a fine one to chain. Take a look at my diagram and see what you think.

I hope that helps - tell me how it goes after a couple more weeks at it.

[velvet]

Thanks that makes sense.

I wanted to ask how exactly does the 180 test taker actually setup a generic binary/in-out game? Like does he/she just take a look at the conditions and start with the logic chain, or does he/she write out all the conditionals and contrapositives before beginning the chain? Even though it eats up precious time, I feel like writing out all the conditionals and contrapositives will help one avoid making mistakes on the actual diagramming of the logic chain.

[noah]

I can't say what the 180 person does, but what I do is write the rules in the chain as I get them, choosing my next rule by looking for one for which I already have elements in the chain.

At first many students do what you say and write out the rules, but you will probably find it unnecessary after a while. Perhaps for some really tough rule you might go back to that, but you'll probably be able to handle most any rule after a while (caveat being that some rules are best written to the side b/c they're compound conditionals that will get too messy).