Sometimes I found that to be a help. You can ignore any interpretation where the gems end up in two boxes, since that couldn’t possibly be the case.
One trick I found helpful is that sometimes you get very limited information about which boxes have the gems. In that case, you can exclude the ambiguous situations. For instance, say only one box mentions the gems at all and says “The gems are in the blue box”. Since there’s nothing to disambiguate the answer if that message was false, then it must be true.
I did fail twice out of 40-something tries. The first was a dumb mistake when I was rushing. The second… well, I forgot to write it down, but I don’t believe I made a mistake. I wonder if it actually had an ambiguous answer.
Yeah, two keys is one of the upgrades. But since I had such I high success rate, I took the upgrade that gives you 3 gems instead. I forget what the third upgrade was.
That is kinda funny about the coat check thing. I guess you could do it without that upgrade, if you got the room that allows duplicate rooms, and thus two coat checks and two stored keys. Or is coat check storage shared?
A more spoilery thing about keys in general:
You can only have one basement key at a time. If you check it, the antechamber pedestal is empty. Kinda annoying since I needed that key and was getting bad luck with the coat checks.
Felt very stupid today after many runs figuring out that the pump room works without being powered up. You only need to power to fill up the giant tank. After that the rest of the motors work fine.