# Reply To: PT77 Game 3

November 14, 2017 at 12:56 pm #3348
Mike Kim
Keymaster

Hi John —

That is a very difficult and unusual game —

In general, you can expect one game per section (occasionally two) to feel markedly more difficult than the others.

But, depending on how you choose to think about games, most tests do not have games that I would describe as being “unusual” — this is certainly a prime example of one of them —

On my end, this is also a type of game that I would expect the test writers to utilize more of, and I’m a bit surprised they don’t. It tests the same things all other games do, but in a way that, I believe, makes it more difficult for students to prepare for.

To me, two of the things that make this game unusual are —

1) It is extremely backended —

I often talk about games as being frontended (designed so that you are meant to make a lot of inferences upfront) or backended (designed so that you are meant to make your inferences down the line as you are managing q’s).

We are given very limited information upfront, and it’s not given to us in a way where we can make a lot of inferences — it just feels like a ton of options to keep in mind.

2) It requires what I would describe, for lack of better wording, as multi-dimensional inference-making, whereas almost all other games and q’s just require linear inference-making —

I know that makes no sense —

What I mean is that this game requires you to think about how different groups of multiple options relate to one another (“If J will pick from one of these two and L will pick from one of these two and P will pick from one of these two, what can I infer from all of that?”) —

And most other games are designed so that you figure out one thing which leads to another which leads to another and so on in a chain (“If X can only be in 2 or 3, but Y is in 3, then X must be in 2, which means Z must be in 5, which then means K must be in 6 or 7, etc.).

In terms of diagramming, I see a couple of options —

1) Just write out the information as given, and not anything else.

There really isn’t anything to write. I do think that in this case you want to spend a lot of time upfront thinking about and trying to see patterns / limited options for how the elements can end up being placed —

For example, two things I noticed were

a) X or Y has to be first element no matter what.
b) no one really wants W, and it’s going to end up near the end no matter what (and the only way for it to not be last is if L chooses it before then).

For a backend game like this, if you can’t get a lot written down up front, at the least you want to make sure you are comfortable playing around with the elements and thinking about how they can end up relating to one another, and again, I would encourage you to give yourself some time to do that before going in to the q’s.

2) Create 4 frames — 1 each for if J, L, P, or T get to pick first.

Mathematically speaking, there are only six total ways to place three things in order, but 24 different ways to place 4 things in order —

By putting one element down, we greatly reduce the amount of uncertainty we have to deal with.

Once I created the four frames, I then rewrote the order of options for the remaining three elements in each frame (to right of picture).

Doing so happened to uncover a massive number of inferences that break the game wide open.

Maybe someone else could have seen the outcome sooner, but I personally did not see these inferences until after I’d written the limited options down for each frame (got a bit lucky).

HTH — btw, even though the second option makes the game easier, I think it’s great practice to try and master this game without frames — so that you know that you can survive either way —

Let me know if you have any follow-up —

MK