Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is an Advanced Linear Game: Balanced.

J98_Game_#4_setup_diagram 1.png

This game features the Separation PrincipleTM. The Separation Principle applies when variables involved in not-blocks are placed into a limited number of spaces. For example, suppose two boys are placed into three chairs, with a rule that the two boys cannot sit next to one another. The minimum amount of room needed to comply with the not-block rule is:

J98_Game_#4_setup_diagram 2.png

Since the minimum requirement happens to be the same as the number of available spaces, the boys are forced into spaces 1 and 3:

J98_Game_#4_setup_diagram 3.png

Now suppose we expand the scenario to four boys being placed into seven chairs, still with the rule that no boys can sit next to each other. The minimum space required by the not-block rule is:

J98_Game_#4_setup_diagram 4.png

Again, the minimum requirement happens to be identical to the number of available spaces, and the boys are forced into spaces 1, 3, 5, and 7:

J98_Game_#4_setup_diagram 5.png

This scenario is, of course, identical to the one in this game, with the boys representing the dance tunes.

[Xantippe]

I did not think to use the separation principle for the initial set up to this game, but I did use it for testing my answer choices.

So, the rationale for starting with a D instead of a B for the first day is because we could have ended up with a BBBBB... forever and a day unless the rules told us otherwise? The rule of separation in the game tells us D's are not consecutive, not that a B has to be between each D?

Sorry if I am asking the obvious, I am trying to get more efficient with games, and using the separation principle in my initial set up may have helped me get to the correct answers quicker.

Thank you.

[Dave Killoran]

Hi Xantippe,

I suggest you play around with the seven spaces and four dance tunes, and see what's possible! Make a few different diagrams, and try to put a ballad first, then try a dance tunes separated by more than a space, then try something else besides a balled as a separator (hint: there are no other choices), etc. You will quickly see that there is simply no other configuration possible other than 1-3-5-7 for the dance tunes, which then forces the three remaining ballads into 2-4-6. I can say that over and over again but it won't hit home until you try to break that scheme up—once you try to, you will see why it has to be that way. So, make some diagrams and I think that's the best way for this idea to really be clear.

Good luck!

[Xantippe]

Ah, got it Dave!

Thanks again for explaining what should have been obvious. I got lost in the forest.

[twendell]

Where are the R/X and S/V double options derived from?

[Adam Tyson]

Happy to elaborate on those for you, twendell!

For that first spot, we know it has to be a dance tune (RSVX), in order to keep the four dance tunes away from each other. Because H is somewhere before V, we know that V cannot be in that first slot. So what about S? If we put S 1st, then V must be third, because of the required S/V spacing (exactly one thing between them regardless of their specific order). Now which dance tune goes 2nd? Well, S must be next to F, so F has to go there, but H has to be before V, so H has to go there. Conflict! When we put S first, we are going to have to break at least one of the rules, and so S cannot go first. That leaves only R or X to take that first spot.

Now let's take that a step further. Where can the S/V block go, if neither is first? There are only two options for the block (and for now we can ignore the order of S and V - it's just about the numbered spaces to fit it in.) Again, remember that the dance tunes (including S and V) must be in the odd numbered spaces. So that S/V block is either in spaces 3 and 5, or else in spaces 5 and 7. No matter what, that means one of S or V has to be in space 5! To place R or X in that spot would break up S and V into spaces 3 and 7, which cannot happen due to their required spacing.

The first inference about the first space leads to the second inference about the fifth space. Get one, and you'll get the other shortly afterwards. That's the domino effect of rules and inferences in logic games that makes it so important to experiment with the rules before diving into the questions!

[CodeyD29]

Happy to elaborate on those for you, twendell!

For that first spot, we know it has to be a dance tune (RSVX), in order to keep the four dance tunes away from each other. Because H is somewhere before V, we know that V cannot be in that first slot. So what about S? If we put S 1st, then V must be third, because of the required S/V spacing (exactly one thing between them regardless of their specific order). Now which dance tune goes 2nd? Well, S must be next to F, so F has to go there, but H has to be before V, so H has to go there. Conflict! When we put S first, we are going to have to break at least one of the rules, and so S cannot go first. That leaves only R or X to take that first spot.

Now let's take that a step further. Where can the S/V block go, if neither is first? There are only two options for the block (and for now we can ignore the order of S and V - it's just about the numbered spaces to fit it in.) Again, remember that the dance tunes (including S and V) must be in the odd numbered spaces. So that S/V block is either in spaces 3 and 5, or else in spaces 5 and 7. No matter what, that means one of S or V has to be in space 5! To place R or X in that spot would break up S and V into spaces 3 and 7, which cannot happen due to their required spacing.

The first inference about the first space leads to the second inference about the fifth space. Get one, and you'll get the other shortly afterwards. That's the domino effect of rules and inferences in logic games that makes it so important to experiment with the rules before diving into the questions!

That was an awesome explanation, thank you!

[yenisey]

The last rule here states: F must be played immediately after R unless G is played earlier than R. I wrote it as If not RF then G- R. The contrapositive will be if not G- R then RF. Does it mean here they both can happen??

AS I know when the sufficient condition is negative, at least one of them has to happen but that doesn't mean both can't happen at the same time right ?

[Robert Carroll]

yenisey,

The rule itself does not prevent RF and G R from happening at the same time. As with any conditional, unless there is some outside restriction, the sufficient condition can be false and the necessary condition be true at the same time.

Robert Carroll