Hey Emmags,
Thanks for the question, and welcome to the Forum!
This is an interesting game, with both Linear and Grouping elements, so it's testing your ability to make some sequencing inferences as well as (from the last rule) some inferences about the UY or UZ groups.
For a setup, use the three spoonfuls as a base labeled 1, 2, and 3, and recognize the two possible unfixed distributions: 3-2-1 (groups of 3 letters, 2 letters, and 1 letter) or 2-2-2 (all spoonfuls have 2 letters each).
Then the rules establish two separate chains:
T > U >= X (meaning T ahead of U and X, and U either ahead of X or in the same group, hence the "=" part of
the chain: X cannot be before U, but they can be "tied")
W > Y (meaning simply that W is in an earlier spoonful than Y)
Lastly, we know that U must be with either Y or Z, but not both, so a UYZ "block" is impossible.
There are a few Not Laws for the first and third spoonfuls, namely that U, X, and Y cannot be in 1, and T and W cannot be in 3. These come directly from the two sequences listed above.
And that's it! So you're correct that the setup so far is a pretty straightforward one...the trouble then seems to have arisen from a mistaken assumption about Y and what it can/can't do.
For Y, we know that it
could be grouped with U (if Z isn't), and we know that it must be later than W, but that's all we can know! So there's nothing that prevents it from being single, so long as U is with Z and the last rule is satisfied, and Y is not in 1 (to keep it after W).
The lesson then is two-fold: (1) Real trouble in games comes not from omitting some truth or having a partially incomplete setup, but rather from presuming truths that are, in fact, not necessarily true (or entirely false). If you hadn't noticed that, say, Y cannot be in 1, you could totally survive that omission and likely would discover it early on in the questions, updating your diagram as you did. But mistakenly thinking that Y cannot be alone, or that T must be in 1 (another common mistake here), or X must be in 3...those are really punishing errors that wreak havoc in the questions. So focus, always, on ensuring that the things you believe to be true are genuinely, inescapably true. (2) If you have included some mistaken truth (found an "inference" that isn't legitimate), the questions should alert you to it. Question 19 in this case should have stopped you dead in your tracks and forced you to immediately return to the rules and your setup and reevaluate everything there. This is a good thing! It means there are safeguards against you working through the entire game with errors in your setup, since trouble (or even outright contradictions) in the questions is a clear sign that you've made a mistake and need to fix it asap before attempting any more of the problems.
Specifically for 19 here, if Y is alone it must be in either 2 or 3, and U must be with both Z and X (if U isn't with X then T, U, and X are in 1, 2, and 3, respectively, and there's no empty spoonful for Y to take solo). That puts T and W together as our twosome in this 3-2-1 distribution, and they must go into the first spot. The variability is with the Y and the UXZ groups in spoons 2 and 3, and sure enough that's what answer choice (D) represents: X could be in 2 with U and Z, with Y alone in 3.
Lastly, the reason you had
some success is because your inference about Y never being alone likely didn't factor into every question, and was only partially wrong to begin with: Y can be alone, or it can be with others. This is different than a mistake like "Y must be in 1," which is not just partially wrong, but entirely impossible. That's a more egregious error and would almost certainly lead to problems for just about every question
So this is a great lesson to learn, and one that I hope not only sticks with you, but also helps you to spot future instances of mistakes and compels you to rectify them quickly and decisively.
Thanks again and please let me know if you still have questions!
Jon
