PT 33. S4.Game 3 Forum

[corgiterrier17]

Hi,

Do you guys recommend figuring out any possible distributions up front? Because when I did this game during the test, I thought about figuring out the distributions first but then I was like, "what if the conditional rules (not both rules) contradict some of those distributions? So I did not attempt to figure out the distributions but it turned out this game would've been much easier if I did.

Possible distributions are:
t s r =6

3 3 0
3 2 1
3 1 2
3 0 3
2 2 2 --> violates conditional rule
2 3 1
2 1 3

so we have 6 possible distributions.

How can I be sure that those 6 distributions are NOT contradicted by the conditional rules?

[180pedia]

If I get what I think you are asking, you don't necessarily. There's not necessarily an easy way to know that distribution #X#Y#Z doesn't work because of this rule interacting with that rule. That was why I often missed min/max questions during my early studies. I would think this answer makes sense without considering some convoluted chain of rules that actually makes it not work. To compensate, I always test up and down on my initial suspicion for min/max now. You shouldn't assume any distribution necessarily works until you prove it does.

Granted, there should be certain distributions you know that do not work. For instance, you should know that all four topazes cannot be selected because of the third rule (which you did) and that 2 2 2 violated the second rule.

t s r = 6
3 3 0 --> X and Y are selected
3 2 1 --> X and Y are selected
3 1 2 --> X and Y are selected
3 0 3 --> X and Y are selected
2 2 2 --> violates conditional rule
2 3 1 --> at least one of X or Y
2 1 3 --> at least one of X or Y

One thing I would note that (if you didn't have it) you should have an X column which is equal to 4. You should always have a not selected group. I don't think this game really requires absolute intimacy with the possible distributions but just how they play together

Question #13 doesn't require distributions. Simple rule application gets you there.
Answer D

Question #14 is more of an abstract type deal...
I'd glance past ABC initially, as D&E strike me as unusually worded and the fact that GJX all have an equal variably in the game make me skeptical of them ever having to be a MBT. We then get to D and E. I like E from a testing standpoint, because it plays with T quite well since T only has two options.
3T->Great, this works.
2T->Four slots left. It'll either be 3-1 (if so, great) or 2-2 (hm, this wouldn't work then). Oh wait, 2-2 can't happen because of rule two.
Answer E

Question #15 local rule
Zt --rule three--> no Wt --rule four--> no Ms (eliminate A, B, and C as all require M) --> eliminate D, because No R with T being 36 at most is the same exact thing as A.
Answer E

Question #16
Exactly two rubies --rule two--> either one or three sapphires (cannot be three, because then there would only be one sapphire)
Answer D

Question #17
Answer D - upfront inference for me. This one should be readily apparent. We have to have at least two Topazes and we cannot have both W AND Z, so we must have at least X or Y in any situation.

Question #18 local rule (we learn a lot from this one)
Js & Ms --rule four--> Wt --rule three--> no Hr and No Zt
no Ks (2xS) --rule two--> ex. one F/Gr (not Hr)
Remember, we only have four out slots which are now filled by Hr, Zt, Ks, and _r
in | out
S: Js Ms | Ks
R: F/Gr | G/Fr Hr
T: Wt Xt Yt | Zt
Answer B

Sorry - super long winded and the latter part probably isn't what you were looking for. TLDR, I don't think knowledge of all the possible distributions is necessarily as important as you think (at least for this game)... it's more important to understand how the rules limit the distributions of other variables and interact. I wouldn't worry about having every single distribution up front. Just remember that the written distributions you come up with are not necessarily proven nor are they exhaustive.