Setup and Rule Diagrams

[ArizonaRobin]

I tried this one using templates, just to see how I would do. I finished it in 10:48, which was okay after finishing the previous game in less than 5 minutes. I missed one question and when I reviewed it and realized I probably should have fleshed out a couple of my templates a little more. It is difficult for me to tell from the outset of a problem if I should create templates or not. Any tips on making that decision?

[Jeremy Press]

Hi ArizonaRobin,

This is a great question that we cover at some length in our Logic Games Bible. It's in the chapter called "Advanced Features and Techniques," in a section labeled "How to Recognize Limited Solution Set Games." I only mention that in case you have the Logic Games Bible, that way you can read a detailed rundown there in addition to what I'll say.

Echoing the Logic Games Bible, it's important to realize there is no single game type or rule type that lends itself automatically to the use of templates. There are often a combination of limitations built into the scenario and rules in the game that constrain the number of outcomes. There are several basic factors to pay attention to. First, watch for numerical limitations. For example: a small number of variables or available spaces; OR a set of rules that fix the positions of large numbers of variables either absolutely or relative to one another and that therefore leave only a few variables free to move around. Second, watch for "duality." For example: a variable that can only be in one of two slots, or a slot that can only have one of two variables. Third, watch for a large number of disparate rules, particularly where a variable shows up in multiple rules (three or more). Fourth, watch for a "space taking" element in the rules, such as a very large and unwieldy block or sequence of variables. These are the most common elements you'll find in templating scenarios, and it's often a combination of two or more such factors that tips my hand to look for templates.

More specifically, this game is a great example of a "Pure Sequencing" game (i.e., a linear game where all the rules are generic sequencing rules) that often lends itself to templates. In most Pure Sequencing games, the rules will allow you to create a "master chain" of variables that includes all (or all but one) of the variables. Here, the rules don't let us create such a "master chain." But, if we follow the "either-or" possibilities inherent in the last two rules, we can use the combinations inherent in those possibilities (plus the first rule) to create the 4 different possible "master chains." This is an infrequently used structure for Pure Sequencing games, but if you ever run across a Pure Sequencing game where the rules don't naturally lead to an all-inclusive (or almost all-inclusive) master chain of variables, you should be on the lookout for templates because they're likely to be operative in such a game.

I hope this helps!

Jeremy

[cmnoury1221]

Hello,
Using Rules 2 and 3 I believe I was able to get the 4 master chains?

JPMLGV
VGPMLJ
GPVMLJ
JPMLVG

Is it worth it to just move the PML chain around for this question, and just fill in the other variables? Or faster to make chains as I did using the variations of rules 2 and 3.

Thank you!
Carolyn

[Paul Marsh]

Hi Carolyn! Attempting to map out every possible template is a good instinct, since it can be a powerful tool to solving Limited Solution Set Games. When it's possible to write out in fairly complete detail each possibility for how the game could play out (think 4 options or fewer), then drawing out each template is usually a big time-saver.

However, for this game there are just too many possible orders for the variables to narrow it down to four precise templates. The 4 examples that you provided are indeed possible orders for the variables, but there are also many, many others. For example, PMLJGV is just one such other order that satisfies the rules.

The best we can do here is to make 4 of what I'm going to call, for lack of a better term, "quasi-templates", where we have a rough idea of some of the order. Those 4 "quasi-templates" represent the 4 different possibilities given to us by rules 2 and 3. I'll think through all of those briefly below.

1) G is ahead of J and L, and V is ahead of G and P. In that case, we know V is first and L is last, with P<M and G<J somewhere in the middle.

2) G is ahead of J and L, and V is after G and P. In that case, we know G or P is first, and one of V/J/L is last, with M hanging out somewhere in the middle.

3) G is after J and L, and V is ahead of G and P. In that case, we know one of V/J/P is first, and G is last.

4) G is after J and L, and V is after G and P. In that case, we know that J or P is first, that V is last, and that G is second to last.

So I don't have four exact templates, but I have four general ways that this game can unfold.

On test day, I likely wouldn't take the time to write all four of those out explicitly. However, in between finishing my diagram and proceeding to the questions, I would take probably ~30 seconds to think through those possibilities in my head and start to get a sense of where the variables can end up (e.g. "Ok, I know that V can be way up front, or all the way in the back...").

Hope that helps!

[cmnoury1221]

That's very helpful, Paul!
Thanks