This question is hard, but the resulting deduction is incredibly useful for the rest of the game. The easiest way to find the right answer is to create a scenario or two to disprove wrong answer choices.
A-D are wrong. We don’t need G, J or X. And, we don’t need one stone selected from any type. This scenario proves all of those answers wrong:
Feel free to read through the rules to try to prove me wrong, but this scenario obeys all of them.
E is CORRECT. It turns out, we always need at least one type of stone to have three stones.
Let’s try our best to create a counterexample. I’ll walk you through the process I used to solve this question on my own. So we want to try to make a workable scenario, where we don’t have three gems of any one type. If we can’t, we know this answer is right.
Let’s look at sapphires. Obviously we can’t use three: that would help prove what we’re trying to disprove.
If we have two, then we have one ruby (rule 2). That means we need three topazes to make six gems. D’oh!
That didn’t work. Let’s try one sapphire instead.
We need five other gems. We can’t have all four topazes, because W and Z can’t go together. So we can try two topazes.
So far we have one sapphire, and two topazes.
We can add two rubies (we can’t use three, because we’re trying to avoid that). But that still only makes five gems.
So there’s no way to get six gems without having three of at least one type. This happens because we can’t have all four topazes.
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