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Remember to bear in mind that at least 1 will always be true, and at least 1 will always be false. So with the blank one there, that means the other two are the false and true boxes.
The first clue would be true if the gems were in either the blue or black boxes. The second clue would only be true if it was in the blue box.
Thinking about it some more if the gems were in the blue box it would make both of them true. Which would invalidate the one must be false rule. But the blank box through me off. I wasn't sure how to evaluate it.
"There will always be at least one box which displays only true statements.
There will always be at least one box which displays only false statements."
Imagine there are three men in a room. You are told that one only speaks honest words and another only lies. But if a man isn't saying anything, he could be either one. A blank box could be either one.
Note the different between "says a true statement" and "all statements they say are true", the first requires a statement and the statement to be true, the second does not require a statement.
If the man (or box) makes no statement at all, he (or it) does not break the rule as written.
But you know what, if you didn't read the rule the first two times, you're not going to now. Have a lovely day.
Blue box = true
If the black box is false, =the gems are not in the blue box, but it could be in the blank box.
However, because there has to be one true statement, it has to be blue because the blank box is not making a statement, therefore the gems are in the black box.
One of the boxes has to be lying. Saying nothing at all is not lying any more than somebody can lie to you while they're asleep, therefore the white box with nothing on it doesn't count. Now suppose it's the blue box: then the gems cannot be in a box with the word blue in it. BUT the black box says that the gems are in a box that is blue, which can't be true because of our assumption. So where's the box that's telling the truth? It can't be the black box, and it can't be the white box either because it's not saying anything. You have a contradiction with the above assumption, which means that the blue box has to be telling the truth.
Now of course you're still wondering where the gems are, but remember the part where the white box doesn't count as a liar? That means it has to be the black box lying to you, telling you that the gems are in a box that is blue. The black box has the gems in it.
If I say I "only eat Italian food", that does not mean I am always shoveling Italian food in my mouth every second of every day.* It means that when I eat, I eat Italian food. If I am not eating anything at the moment, it can still be true that I only eat Italian food.
*Though sometimes I wish I could. It's so delicious!