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Are there any important inferences I needed to make? I tried to look over the possibilities based on whether U was in the same spoonful as Y or Z.
General Rules
T < U ≤ X
W < Y

Possibilities (Given that Z is Random)
WT < UY < X
T < W < UYX

WT < UZ < YX
 Adam Tyson
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Z isn't really random here, LSAT20148, because it is in the rule about U having to be paired with something. Other than that, I think you're looking pretty good here! You've identified the numerical distributions of 2-2-2 or 3-2-1 (unfixed).

I think you will find that there are many more possibilities to this game, and I wouldn't chase them all down, especially since there are only 5 questions. Don't box yourself in by thinking that these are all there are, but instead use them as a jumping off point to help you understand the game overall a little better. I didn't see any major inferences in this game, and I only chose to do a single hypothetical before heading to the questions. I based it on the 2-2-2 distribution since I saw that it really boxed U in tightly:

T would have to be in the first spoonful, U in the second, X in the third. either Y or Z would go with U. W would have to go with T since it couldn't be in the last spoonful, and then the leftover of Y and Z would go with X in the last spoonful. So it looks like this:

TW - U Y/Z - X Z/Y

Two solutions, one template, and that covers the 2-2-2. For the 3-2-1 I could see that there were too many choices for which group was what size, so I just moved to the questions figuring I'll work those out when and if I need to. That happened, for example, on question 19, where I worked out a 2-1-3 and a 2-3-1 to see what could happen when Y was alone.
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For this question, I started with figuring out which letters cannot go in the first or third spoonful. U,X, Y cannot go in first and W/T cannot go in third. this was my jumping off point. Did I miss any key inferences? I didn't want to spend too much time writing out scenarios and went straight to the questions after this.
 Robert Carroll
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I sketched a diagram out quickly myself on some paper and didn't really see any other inferences. Everything beyond what you said is very conditional, like "If U is not with Z, then W is before U," which is true, but why bother thinking of such a specific case? Most of the questions are local, which seems to bolster the case that minidiagrams for specific questions are going to be the way forward in this game, not an inference-heavy main diagram. The only other choice is a bunch of templates, but Adam showed earlier in this thread why templates are probably too numerous to be useful here.

Robert Carroll

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