Setup and Rule Diagrams

[clarocca]

I understand the explanation provided in the answer explanations. Yet, are there any tips for how you can know when you've written out every possibility? I think I would sit there second guessing whether or not I've realized every possibility and waste a great amount of time.

[David Boyle]

I understand the explanation provided in the answer explanations. Yet, are there any tips for how you can know when you've written out every possibility? I think I would sit there second guessing whether or not I've realized every possibility and waste a great amount of time.

Hello clarocca,

That's a good question. Sometimes you can know easily you've exhausted every possibility, e.g., if you have a group of A and B, and a group of 1, 2, and 3, and you know that there are only six pairs you can make (A1, A2, A3, B1, B2, B3). Sometimes it's harder, as in the present game.
With the m's and s's, one chokepoint is that the fifth load must be an m, "mulch". So given that there are three m's, you can do a "count" of sorts: there's one configuration is possible if all three m's slop over to fill spaces 5, 6, and 7 (so that there's only one changeover); and if you "walk" the block of 3 m's over one space, and then another space, you have m's in 4-5-6 and 3-4-5 respectively (yielding two changeovers).
Then after that, you see what configurations there are when there's no more three-block of m's. There's always the m in space 5, so if it's left alone with no m on either side, the only place the other 2 m's can be is on the far left, together as a block in 1-2. Otherwise, there'd be too many changeovers.
All that's left is if the m in space 5 has an m on either side, If it's in space 4, then the remaining m has to be at either end, 1 or 7, or there'd be too many changeovers. Similarly, if the m is in space 6, then again, the only place the last m can be is in space 1, to avoid more than three cleanings. (The last m can't be in space 7, because we already used up the scenario with m's in 5-6-7.)
So if you do things in that systematic way, it helps track things.

Hope this helps,
David

[clarocca]

Thank you David! Very thorough and helpful. I will try to do my best to work systematically. I think that is a very good piece of advice.

[mariahenain]

I'm having a lot of trouble with this game... I think it's because of the lack of rules and the nature of the game itself. How can I ensure I'll have time to do all 7 set ups? Is there a more simplified way of viewing this game?

[jenna_d]

The explanation of this game makes it seem relatively easy, yet how can we avoid tricks like not putting the cleanings into separate categories? I really tripped over this game and feel like I let a pretty easy game ruin me on this test! Additionally, considering how many different scenarios there are, about how long should a game like this take? Thanks!

[Adam Tyson]

Nobody should say this game is easy, Jenna! At least, not without adding "if you understand the thing about the cleanings", because that's where most people get lost. How do you know that the cleanings are a restriction and not a variable themselves? By recognizing that they don't happen IN a slot, the way the loads of mulch and stone do, but BETWEEN slots, limiting how many times you can switch materials. It might help to glance at the questions and see that they talk about the loads and not the cleanings, except for one question that asks not about when you can clean the truck bed but only about how often. That should suggest that the cleanings aren't variables after all.

As far as knowing when to stop, the systematic approach David described should help - try all 3 Ms together every way you can, then try a pair of Ms with another separated from them, and finally consider splitting them all up (which will not work). When you've tried everything like that, in an orderly and systematic approach, you'll know when to stop.

The bigger question in my mind is, how do we know to take this approach in the first place? It's rare to just go after all the possibilities, and potentially a giant time suck. My personal guideline is this: do it when you've got nothing else! If your diagram is a big empty space, and/or you've spotted no obvious inferences, it's time to try something. Maybe that something will turn into a few templates, or perhaps it will turn into all the solutions as it does here. You won't know until you start down that path. When all else fails, start thinking with your pencil instead of with your head.

Thankfully there aren't many games like this one, but now if you see one you stand a good chance of knowing what to do.

Good luck, keep at it!

[jenna_d]

Thank you! Very helpful!

[Etsevdos]

Got through this relatively quickly without breaking out into 7 - seems a bit time limiting. General thoughts on not breaking out?

[Adam Tyson]

I've seen a few people who sketch out one or two solutions, etsevdos, and then they make the key inferences (at least two Ms always together, and if they are not all together then at least one is on an end), and then they are good to go, but I find that most folks will take too much time on the questions, sketching things out again anyway. If you are able to manage it in your head without doing that, then by all means do so! Just be sure you aren't getting over-confident. A good diagram is never a bad thing, as long as you do it in a timely manner. The other games on this test were not so time consuming, so I feel like there should be plenty of time to nail it down for this one. There's no bonus for finishing early, after all (unless it's that you get to run to the bathroom).

[SwanQueen]

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.

Hello!

I was wondering, what was your strategy to establish that the best avenue was to write out all of the possible solutions, and how did you know that there were only seven solutions in total? How did you go about getting to this point?

Thanks in advance!