Setup and Rule Diagrams

[Adam Tyson]

My decision to take this approach, SwanQueen, was based on having nothing else to go on. Having gone through the original rules I found myself staring at a fairly empty linear base with virtually no inferences, and when that happens it can be dangerous and time consuming to plow ahead into the questions. In cases like this, I find it's best to simply try something, come up with one workable solution, and see if that starts to generate some inferences. This can lead to creating a few templates, or several solutions, or in some cases to recognizing that there are too many possible solutions and that it might be a good idea to just forge ahead and apply brute force to the questions.

I didn't determine that there were 7 solutions until after I had done them all! The process was something like this:

"Hmmm, I don't see many inferences, but this 'cleanings' restriction looks important, so let me try something. Can I alternate mulch and stone a bunch of times? No, that will be too many cleanings, so I have to keep some clusters of each together. I know an M is 5th, so let me try putting all the Ms together around that spot. How many ways can I do that?"

"Okay, I found a few ways to make that work with the Ms all in a bunch. Now can I try splitting one of them off from the other two? How might that work. This is taking a while, but it feels like there aren't going to be that many more workable solutions, so I am going to keep going with this."

"One more thing to try, and that is leaving that M at 5 all alone, and taking the other two Ms away as a pair since I now know I can't just split them all up, even if I put the other two Ms at 1 and 7. Okay, that only works one way, so I think I'm done! Let's go crush some questions!"

Identify the Possibilities games, where the best solution is to just draw them all out, are few and far between. You should hesitate before going down this path, and often when you start down it you will find yourself either just doing templates or else you will abandon the approach as soon as you realize that there are too many solutions to make it worth chasing them all down. But there will be times, like with this game, when the process should be carried to the end and the results will be very beneficial, leading to a very rapid and completely accurate run through the questions, followed by a little happy dance in your chair!

[baxleyce]

Hi, I am confused as to why the setup SSSMMSM is 3 cleanings? If I represent the cleanings with a "|" i assumed the cleanings would be : SSSM|MS|M. Since the M on the outside is not accompanied with an S and was cleaned right before it I figured there wouldn't be a cleaning after it, making there be only 2 cleanings instead of three as diagrammed in the setup outline.

Could anyone explain why did qualifies as 3 cleanings according to the game? Thanks!

[baxleyce]

Setup and Rule Diagram Explanation

This is a Basic Linear: Balanced, Identify the Possibilities game.

This game can be confusing if not approached correctly. However, if you take the right approach, this game is quite easy. The critical question is how to handle the cleanings: should they be a separate variable, such as C? Should they be their own row, making this an Advanced Linear game? The answer, interestingly enough, is neither. Making the cleanings a separate variable set greatly increases the difficulty of this game. Instead, treat them as non-variables, and simply note when the materials change. This allows you to approach the game in a Basic Linear alignment. Here is how that diagram appears, with the second rule diagrammed on the setup:

powerscore_M12_T3_J2010_LG_explanations_game_3_diagram_1.png

While we will not treat the cleanings as a separate variable set, they are incredibly important to this game, and quite restrictive. Because the cargo bed cannot be cleaned more than three times, this means that you cannot have MS or SM appear more than three times. Let us consider how that affects the order of the loads.

• 1. If there is exactly one cleaning
  
  If there is only one cleaning, the materials must be in continuous blocks; that is, each type of material must be hauled consecutively, with a single cleaning in between each group of materials. This would normally present two possibilities, but because the second rule stipulates that the fifth load is M, there is only one solution when there is one cleaning:
  
  powerscore_M12_T3_J2010_LG_explanations_game_3_diagram_2.png
  The single cleaning occurs between the fourth and fifth loads.
  
  The templates are numbered on the left for easy reference.
  
  2. If there are exactly two cleanings
  
  If there are exactly two cleanings, the following two possibilities can occur:
  
  powerscore_M12_T3_J2010_LG_explanations_game_3_diagram_3.png
  3. If there are exactly three cleanings
  
  If there are exactly three cleanings, the following four possibilities can occur:
  
  powerscore_M12_T3_J2010_LG_explanations_game_3_diagram_4.png

Thus, there are only seven solutions to the game, and having those seven solutions makes the game easy. But, as always, it is a matter of getting to that setup before the game becomes easy.

Sorry for the additional question but how come MS|MS|MS|S isn't an option for 3 cleanings (with the "|" designating the cleaning)?

[Poonam Agrawal]

Hi baxleyce!

Let me start by addressing your first question. The game scenario says that the truck must be cleaned in between any two loads of different materials, which would mean between any S and M in your diagram. Stone and mulch are the two different materials in this game.

SSSMMSM is three cleanings like so: SSS | MM | S | M

As for your second question, MS | MS | MS | S doesn't work as a solution to this game because you have to clean between every M and S. That type of diagram should look as follows: M | S | M | S | M | SS, which is actually five cleanings.

The trick to this game is understanding that a stone load and a mulch load can only be hauled consecutively if the truck is cleaned in between. I hope this helps!

[baxleyce]

Poonam,

Thank you so much that helps clear things up a lot! Misinterpreting the cleaning rule threw me off a lot but it makes a lot more sense now.

Caroline

[QueensULawHopefully]

How does this game's set up differ from the 'headquarters' part of the mining game in PT 86 (Game #3; November 2018)? They seemed ever so similar when I read the stimuli. Moreover, I got even more confused from this game as I went to set it up like I did for PT86's game. So basically I started doing MORE than 7 spots because I thought the cleaning would take up a spot as it did in the mining game (In the mining game I designated a "X" for when they'd break at headquarters). Is the reason the 'cleaning' variables didn't count as a 'spot'/variable in PT60's game because the stimulus directly said exactly 4 stone and exactly 3 mulch?

[Beatrice Brown]

Hi QueensU! Thanks for your great question

The difference between this setup and the mining game in PT 86 is that in the mining game, a visit to headquarters counted as the visit the team made for that month (making H one of our variables). In this game, the cleanings are not one of our loads. Instead, we can thinking of the cleaning as a constraint on the ordering of our loads. Although headquarters acts similarly as a constraint in the mining game (because visits to H must happen between trips to different mines, just like cleanings must happen between different load types in this game), it is also a formal variable because the base was visits, and headquarters is a visit. In this game, our base is loads, and cleanings aren't a load, cleanings are not a formal variable.

So, the main difference between the two is that in the mining game, headquarters was also a variable because of what our base was. In this game, cleanings are not a variable because our base is the seven different loads, and cleanings aren't a load. Instead, in this game, the cleanings act just as a constraint on how our loads can be ordered.

I hope this helps, and let me know if you have any other questions!