Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Defined-Fixed, Unbalanced: Overloaded game.

There are initially nine possible shirt options: the three sizes in each of the three colors. The rules that indicate that no small red shirts and no large blue shirts are available leave only seven shirt types for Casey to choose from:

J92_Game_#2_setup_diagram 1.png

Thus, this Grouping game is reduced to selecting three shirts from a pool of seven total shirts. Because Casey cannot purchase both a large and small shirt, and there are not three small shirts or three large shirts available, it follows that Casey must always purchase at least one medium shirt:

J92_Game_#2_setup_diagram 2.png

This inference is one of the keys to the game, and is the only significant inference that most people draw based on the game scenario and rules.

In a game such as this one, where there are very few inferences but not apparently a large number of possible solutions, an excellent approach is to make a few hypotheticals before attacking the questions. That can help you discover the medium shirt inference above.

[HasanT]

I gave it a few days to try and forget the problem and upon revisiting it I am still stuck.
Initially I used the colors as a base; however, my diagram was oriented differently than the one on this board.
Rl YL xxBlxx

RM YM BM

xxRSxx YS BS


I will try using the inference you mentioned but the language of these questions seems to have me baffled.

Does " Casey does not buy both a small shirt and a large shirt" mean she can not buy a large red/yellow and a small yellow/blue?

[Ricky_Hutchens]

Hi HasanT,

That's right, Casey cannot do any of the following:

LR LY SY
LR LY SB
SB SY LR
SB SY LY

Any time there is a small there cannot be a large and vice versa. This is how you know that at least one of the purchases must be a medium, because the other rules make it so that there are only 2 possible small shirts and two possible large shirts.

As far as your diagram goes, it lists all of the possibilities correctly.

If you have anymore questions just keep posting them here.

[PB410]

Hi Dave,

I watched a couple different explanations of this game, and I completely missed the inference that at least one shirt must be medium at all times. Is there a lesson from the Power Score bible I can review or is there some further explanation you can offer that will allow me to recognize similar patterns in other games?

Thanks.

[Francis O'Rourke]

Hi PB,

I would recommend reading over the subchapter How to Recognize Limited Solution Set Games from Chapter 9 of the Logic Games Bible for additional help with this type of inference. In fact all of Chapter 9 will strengthen your ability to find inferences such as this on future games.

[Tajadas]

Hi,

Rule 2 states that 'Casey does not buy two shirts of the same type.'. How could I diagram this? I see rules barring repeats in LG problems often, and sometimes I forget that the rule exists!

Thanks!

[Adam Tyson]

I don't think I would, Tajadas - there are some rules that are just easier to memorize than to diagram, and "no repeats" is that sort of rule. But if you felt the need, you could do something like a not-block or double-not arrow:

Type Type

Since a "type" has been defined as a color and size combo, that means that if you have a Medium Blue shirt, you cannot have a second Medium Blue shirt. A Small Blue might be possible, or a Medium Red, but not another Medium Blue.

Rules that prohibit two variables in the same space, or that prevent a variable from being repeated, are generally the sort that you should just internalize, rather than try to diagram.