Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

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

The game scenario indicates that a bakery delivers exactly six loaves of bread, each with two characteristics: kind of bread (O, R, W) and sliced/unsliced (S, U). Because the loaves are not ordered, this is a Grouping game. The basic scenario appears as follows:

D99_Game_#1_setup_diagram 1.png

Although the sliced/unsliced option could be shown as S and S, in this instance we have chosen S and U so as to avoid any possible confusion over a missed slash. If you represented it otherwise, there is no problem with that.

The first rule establishes that there are at least two kinds of loaves. Thus, all six loaves cannot be of a single kind:


Min 2 kinds


The second rule establishes that there are a maximum of three rye loaves:

D99_Game_#1_setup_diagram 2.png

The third rule states that no unsliced wheat loaf exists:

D99_Game_#1_setup_diagram 3.png

Correspondingly, because all loaves are sliced or unsliced, this means that every wheat loaf is sliced:

D99_Game_#1_setup_diagram 4.png

Because every wheat loaf is sliced, if a loaf is unsliced, it must be oatmeal or rye:

D99_Game_#1_setup_diagram 5.png

The fourth rule indicates that there is at least one unsliced oatmeal loaf:

D99_Game_#1_setup_diagram 6.png

Of course, from the first rule there must be at least two kinds of loaves, and since there is an oatmeal loaf, we can infer that at least one other loaf is rye or wheat, a fact that can be shown on our diagram with a dual-option:

D99_Game_#1_setup_diagram 7.png

The fifth rule is very specific, and states that if two or more loaves are unsliced, then at least one is rye:

D99_Game_#1_setup_diagram 8.png

The information from all of the rules can be combined to form the final diagram:

D99_Game_#1_setup_diagram 9.png

[c-erv]

Hello all,

I am having trouble with this games set up, and looking for some guidence. All I've been able to infer is that there will be (at least) one unsliced oatmeal loaf and a slice of rye or wheat in order to meet the at least two kinds of loaves minimum. After that I am completely lost

[Emily Haney-Caron]

Hi c-erv,

You're right that, from the first rule, you can infer that there will be at least 1 of rye or wheat. Let's take a look at inferences for the other rules.

Rule 2: Since there are 6 loaves total, this rule tells us that there are at least 2 of either wheat or oatmeal (although there could be more of either); if we have 3 rye, we still need 3 more to get to 6, and with only 2 types left, we'd have either 2 of one of them and 1 of the other, or 3 oatmeal since we know we need at least 1 oatmeal (and if we have fewer than 3 rye loaves, we could have more of either wheat or oatmeal)

Rule 4: This means that, if there are 2 or more unsliced oatmeals loaves (since there can't be unsliced wheat), there will be 1 or more unsliced rye

With that, try the game again, and see where you get!

[LSAT2018]

With games that inform you of the minimum and the maximum such as this one, I think it would be difficult to list every possibility. So would an inference be better made using the minimum/maximums instead?

Also would this be similar to game 2 in Practice Test 32, which indicates minimum and the maximum as well?

[Vaidehi Joshi]

@LSAT2018

I did not list out possibilities in this game. My approach to the main diagram for this game was to use a game board of the following type, since this is a bit of an unusual type of grouping game (pretty hard to draw using forum text, I hope you get the gist!)

S | U
--------------------------------------
o | |
--------------------------------------
R | |
--------------------------------------
W | |

And when I diagrammed the first two rules (which are min/max rules), I simply put:
R1: "min 2 KINDS" simply to remind myself that I can't just have all O's/all R's/all W's. it's hard to diagram this rule, so you gotta keep it in your head, I would say
R2: for this one, I just wrote to the side of my "R" row in the game board, "max 3" to keep in mind that I can only have 3 R's put into the diagram

Not really many other options to represent these right off the bat, until we get to later rules

[Jenmstearns]

I’m still stuck on the setup and inferences here. I couldn’t even figure out how to define the rules in a way that I could glean any information from it. What basic components am I overlooking when it comes to working with these minimums and maximums alongside two different variable sets (type of bread and sliced/unsliced)? It all just gets muddled in my head and I don’t know how to untangle my thought process.

Which components do I look at in which order to best make sense of the game? I did six spaced lines for type of bread with a corresponding set of lines above it for slice status, but after putting O with a U above it in one space, I had no notion of what questions to ask myself next to make any progress.

[Dave Killoran]

Hi Jen,

I'm going to have our official setup posted into this thread. I'm not sure why it isn't here yet. Should be Monday AM. Thanks!


Note: setup has been added