Some Parlor games are incorrect/broken.

[Bullhawk]

I just got a parlor game where I had 3 statements on each box.
Blue box states that: "A box with a true statement is empty." "A box with a false statement is empty." "The white box is empty."
White box states that: "A box with only true statements is empty." "The black box is empty." "A box with a statement that is also on another box is empty."
Black box states that: "A box with more than one false statement is empty." "The black box is empty." "A box with no true statements is empty."

Blue box can't be the fully true one, because the first two statements would make every box empty. Which means that either white or black have to be fully true, in which case "The black box is empty." statement has to be true, since it's on both of them. That means that Blue box has to be the fully false box, because the black and white boxes both contain a true statement. I opened the white box, because blue box stated that it was empty, which should've been a lie, but the it turned out to be a truth, because white box was empty.

[ricky1981]

I think your first assumption is wrong.

- "A box with a true statement is empty."
- "A box with a false statement is empty."

These can both be true since they say "a box" not "all boxes".

[Quinbee]

I would say the gems are in the black box.
Blue = All Truth
White = Mixed (1st statement true, 2nd and 3rd false)
Black = All False

I think what tripped you up (from my perspective) is blue's statements. "A box with a true statement is empty" I interpret as "there is a box that has a true statement and it is empty", not that "any box with a true statement is therefore empty"

[BobThePenguin]

I'd also pick the black box.

If black is lying, then all its statements can refer to itself:
- The black box is not empty.
- A box with no true statements is not empty.
- A box with more than one false statement is not empty.

Blue would then be telling the truth:
- A box with a true statement is empty (itself, or white)
- A box with a false statement is empty (white)
- The white box is empty.

White is a mixed bag:
- A box with only true statements is empty (true, white)
- The black box is empty (false)
- A box with a statement that is also on another box is empty (true if referring to white).

[skf_mikeweber]

OK, so I am also picking the black box.
If Blue:
* Blue.3, White.2, and Black.2 are all True, meaning no FFF box. Immediate DQ.
If White
* Blue.3 is false, White.2 and Black.2 are True, meaning Blue is FFF.
* White.3 is always true (either White or Black will be empty).
* If White.1 is true, White is TTT. Which means that White cannot contain the gems.
* If White.1 is false, then Black must be TTT and must have the gems.
*** either way, White doesn't have the gems.
So, Black:
* Blue.3 is true, White.2 and Black.2 are false.
* Blue therefore is TTT.
* White.3 is always true, making Black FFF.
* Black.1 is confirmed to be false (Black has the gems and has more than 1 false statement).
* Black.3 is confirmed to be false (Black has no true statements and has the gems).
* White.1 is true (Blue is TTT and is empty).
* White is therefore mixed TFT.
* Blue.1 is confirmed to be true (either Blue or White)
* Blue.2 is confirmed to be true (White).

[kory]

"A box with a true statement is empty" can be read to mean in general ("a person who climbs this mountain will die" means anybody who tries), or can be read specifically ("A person in a red jacket has the key" means one person has the key and they happen to have a red jacket).
In this game, I think those statements are meant in the specific, not the general, but I really wish they would update to remove those ambiguous statements.

[Haxton]

Predicate logic 101 does help to make the leap here

"A box with a true statement is empty" should be interpreted as "There exists at least one box which has a true statement and is empty"

Then, it's just a 2-step process
Can Blue be all False? No. If Blue is all False then 1st and 2nd statements actually mean "There are no boxes that has at least 1 true / false statements and is empty", i.e. "All boxes that has a true / false statement has gems" which would result in all 3 boxes having gems
Can Black be empty? If Black is empty, then there is no all false box (Blue can't be all false as above, Black and White both has a true statement (Black is empty)), so it has to have gems.