Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Linear: Pattern: Identify the Possibilities game.

The initial scenario and rules provide the following information:

O94_Game_#4_setup_diagram 1.png

The game hinges on the colors produced by combining the flasks. The key is to examine the results that occur when one or two experiments are conducted. Because each experiment combines two of the flasks, and no result of an experiment can be used, there is a limited number of possible outcomes in this game.

If only one experiment occurs there are six possibilities, and each possibility encompasses the results of the experiment and the colors of the other two, non-used flasks. These possibilities are based on the order of the rules, so possibility #1 reflects what occurs when the second rule (which is the first rule that addresses specific flasks) is implemented:

O94_Game_#4_setup_diagram 2.png

If only two experiments occur there are only three possibilities, and each encompasses the results of the two experiments:

O94_Game_#4_setup_diagram 3.png

Thus, there are only nine outcomes (or solutions) to this game, and once you have identified all nine, the questions are considerably easier.

[ajb17]

This game involving flasks gave me quite a bit of trouble. I haven't seen a question type like this, thus far. Is LSAC still utilizing these types of games? Additionally, an explanation would be great. Thanks.

[Dave Killoran]

Hi Ajb,

Has a game quite like this appeared since then? No, there hasn't been anything quite like the Flask game over the years (this game is not unique in that sense; other games that were equally unusual have appeared). However, there have been many games that required the same solution approach--Identify the Possibilities. Thus, the benefit of studying this game is to consider what the optimal solution is, and then to examine the factors that lead to that solution. Because, while this game may not appear again, you can still increase your overall understanding of games by studying it and seeing how the pieces work together.

The solution here is that there are a limited number of outcomes based on the experiments performed. Try to approach the game by identifying every solution (there are only 9 solutions: 6 when there is one experiment, and 3 when there are two experiments). Having those 9 solutions up front makes the game considerably easier

Take a look at that, and please let me know if it helps.

Thanks!

[Arindom]

Hi Dave,

I have encountered weird games before but i am stumped by what the 3 solutions out of 9 are. The 6 solutions when one experiment is formed is - there are already four chemical solutions (red, blue, green, orange in flasks 1, 2, 3,4). The remaining 2 solutions are a)when flask 1 and 2 are mixed together and b) when 3 and 4 are mixed together.
Are the remaining 3 solutions - flasks 3 and 1; 4 and 2.... and I'm lost!!

Could you help out? What do you think are the chances of such a game appearing in June?

Thanks.

- Arindom

[Nikki Siclunov]

Arindom,

Curveballs on the LG section have become the new normal, and so it's entirely possible that a Pattern game could appear again on the June test!

To answer your other question, remember that you have 4 flasks, and each of the combinations presented only mixes the contents of two of the flasks (the product cannot be used in future experiments). So, after conducting one experiment, you will have used two of the four flasks; the remaining two flasks can be used during the second experiment.

The optimal approach to this game is to figure out the combination of colors you'll end up with after conducting one experiment (determine that for each of the six possible combinations presented); then conduct a second experiment mixing the remaining two flasks. Ultimately, you'll end up with 6 solutions (after one experiment) and 6 solutions (after two experiments). The first set of 6 solutions will each present a combination of three colors, one of which cannot be used in the future. The second set of 6 solutions will each present a combination of two colors.

Hope this clears it up!

Thanks,

[avengingangel]

Thanks for the explanations. To back up a bit, the book says, "If only one experiment occurs there are six possibilities, and each possibility encompasses the results of the experiment and the colors of the other two, non-used flasks." Why is that [the other 2 flasks] a part of the explanation / solution? What does the color of the other 2 non-used flasks have anything to do with each experiment of combining the other 2 flasks ?? And, more importantly, what from the game rules indicate that you would need to know that ?? Totally lost on this one. Thanks.

[Adam Tyson]

When we talk about solutions here, angel, we are talking about results - what we have after one experiment, what we have after two experiments. If you mix the contents of flasks 1 and 2, what you have remaining is three things - the contents of that mixture (which is now red) and the contents of flask 3 (still green) and of flask 4 (still orange). That solution (result) is RGO. Note that the order of the flasks is irrelevant - I could just as easily have said that solution was GRO or ORG, etc. The point is that I have one red one, one green one, and one orange one.

If you start by mixing flasks 1 and 3, you get blue, and flasks 2 and 4 still have blue and orange, respectively, for a solution of BBO.

One way to see that this information (about not just the two flasks that were mixed but also the two that were not) is required is to take a quick look at the questions. The first question asks about the colors in the three nonempty flasks, and the answer choices all list three colors. This should make clear that we aren't only interested in the results of the experiments, but also in the leftovers. Also, since the scenario tells us that any experiment involves mixing just two of the four flasks, you should be on alert right away that after one experiment you will have three flasks left and the chance to do one more experiment. You always need to track all the variables, so keep track of those that have been used and also those that have not. In that way this is kind of like an in/out grouping game.

After two experiments you will always have two nonempty flasks left, and the solutions will be about what colors are in those two flasks. If you start with 1 and 2 (making red) and then do a second experiment, you are forced to mix 3 and 4, because they are all that's left. That gives you blue, and so your solution is RB (or BR - makes no difference). Note that if you did those same experiments in reverse order you would end up with the same solution.

Pay attention to all the variables and track them through each iteration of the experiments in order to get complete solutions. Good luck!

[ladistar]

When we talk about solutions here, angel, we are talking about results - what we have after one experiment, what we have after two experiments. If you mix the contents of flasks 1 and 2, what you have remaining is three things - the contents of that mixture (which is now red) and the contents of flask 3 (still green) and of flask 4 (still orange). That solution (result) is RGO. Note that the order of the flasks is irrelevant - I could just as easily have said that solution was GRO or ORG, etc. The point is that I have one red one, one green one, and one orange one.

If you start by mixing flasks 1 and 3, you get blue, and flasks 2 and 4 still have blue and orange, respectively, for a solution of BBO.

One way to see that this information (about not just the two flasks that were mixed but also the two that were not) is required is to take a quick look at the questions. The first question asks about the colors in the three nonempty flasks, and the answer choices all list three colors. This should make clear that we aren't only interested in the results of the experiments, but also in the leftovers. Also, since the scenario tells us that any experiment involves mixing just two of the four flasks, you should be on alert right away that after one experiment you will have three flasks left and the chance to do one more experiment. You always need to track all the variables, so keep track of those that have been used and also those that have not. In that way this is kind of like an in/out grouping game.

After two experiments you will always have two nonempty flasks left, and the solutions will be about what colors are in those two flasks. If you start with 1 and 2 (making red) and then do a second experiment, you are forced to mix 3 and 4, because they are all that's left. That gives you blue, and so your solution is RB (or BR - makes no difference). Note that if you did those same experiments in reverse order you would end up with the same solution.

Pay attention to all the variables and track them through each iteration of the experiments in order to get complete solutions. Good luck!

Adam, how are you able to deduce the specific colors for the remaining flasks after the first experiment? Some of the questions on this game are asking about specific colors after the first experiment, and this part is tripping me up. Thanks in advance!

[Dave Killoran]

Hi Ladistar,

Thanks for the question! This information actually comes from the first sentence of the scenario, which states, "A science student has exactly four flasks—1, 2, 3, and 4—originally containing a red, a blue, a green, and an orange chemical, respectively." So, you have an initial color setup of:

• Flask 1 = Red
  Flask 2 = Blue
  Flask 3 = Green
  Flask 4 = Orange

Thus, for example, when you have Flasks 1 and 2 mixed, then according to the first rule they produce a red chemical. You still have flasks 3 and 4 unused, and from the list above we know they contain a green chemical and an orange chemical, respectively:

• Flask 1 + 2 = Red
  Flask 3 = Green
  Flask 4 = Orange

This is one of those instances where the test makers included some critical "initial settings" information into the game scenario. If you ever find yourself looking at a game and nothing seems to make sense or you can't figure out how to start, one step to take is to re-check the scenario to see if they didn't provide some information similar to that above. It's easy to gloss over the game scenario, and the test makers know that. So, aside from the usual parameter information (such as every variable is used, or that there are no empty spaces, etc) they sometimes include information about how the game itself is initially set up (in this case, the color of the four flasks). If you miss that info, it can be deadly!

Please let me know if that helps. Thanks!

[ladistar]

Hey Dave, that makes sense. I can't believe I glossed over that part so easily. I just went back and saw the word "respectively" in the stimulus... I will definitely be sure to pay extra close attention to the wording in stimulus from now on. Thanks for the help and heads up!