The boxes-and-gems puzzle.

[󠀡󠀡vainquit]

blue: the true boxes are both empty
white: the false boxes are both true
black: the gems are in the blue box

I choose white (in this case I think white=false, black=false, blue=true), and it's empty. Can anyone explain this?

[功夫kappa]

should the second statement read "The empty boxes are both true" ?

[Perpetual]

Ah, both White and Blue are False. White contridicts itself, and blue cannot be true unless black is false, which would mean that there would be only 1 true box, which means Blue cannot be true. So the gems were in Blue.

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Originally posted by 功夫kappa:

should the second statement read "The empty boxes are both true" ?

No, it's not a typo. So it will be false

[rumpelstiltskin]

i think the second statement should be "the false boxes are both empty", since "the false boxes are both true" is unconditionally false

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Originally posted by Perpetual:

Ah, both White and Blue are False. White contridicts itself, and blue cannot be true unless black is false, which would mean that there would be only 1 true box, which means Blue cannot be true. So the gems were in Blue.

Thank you. Now I see where I went wrong. I ignored the word "both," which actually implies that the number of true statements is two.

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Originally posted by rumpelstiltskin:

think the second statement should be "the false boxes are both empty", since "the false boxes are both true" is unconditionally false

Yes, it's false, and It's not a typo. Now I see where I went wrong. I ignored the word "both" in the blue box, which actually implies that the number of true statements must be two, so the blue is false——there is only one true statement, the black

[Dimpl]

I interpreted the inverse of 'The true boxes are both empty' to be 'at least one true box contains gems', which is a paradox. I don't think it's accurate to say that 'the true boxes are both empty' is equivalent to 'there are two true boxes and they are both empty', which seems to be what the game is suggesting.

[󠀡󠀡vainquit]

Originally posted by Dimpl:

I interpreted the inverse of 'The true boxes are both empty' to be 'at least one true box contains gems', which is a paradox. I don't think it's accurate to say that 'the true boxes are both empty' is equivalent to 'there are two true boxes and they are both empty', which seems to be what the game is suggesting.

Great! Your explanation is better!

[Dimpl]

I think your explanation was fine, but this particular puzzle was poorly written.

[Swede]

Edit: I'm sorry, this wasn't the exact puzzle OP posted about, but it was so close that I got confused!

Here are the boxes in question, straight from the game:
https://steamcommunity.com/sharedfiles/filedetails/?id=3468099521
https://steamcommunity.com/sharedfiles/filedetails/?id=3468099387

Blue: The empty boxes both have true statements.
White: The blue box has a true statement.
Black: This box contains the gems.

Possible non-contradictionary true/value combinations:
T F F: invalid, blue and white are both true or both false
F T F: invalid, blue and white are both true or both false
F F T: invalid, if black is true, blue and white are empty and thus both true
T T F: invalid, if blue and white are empty, black contains the gems and is thus true
F T T: invalid, white and blue are both true or both false
T F T: invalid, white and blue are both true or both false

As far as I can tell, there are no valid answers at all here.

[󠀡󠀡vainquit]

Originally posted by Swede:

Edit: I'm sorry, this wasn't the exact puzzle OP posted about, but it was so close that I got confused!

Here are the boxes in question, straight from the game:
https://steamcommunity.com/sharedfiles/filedetails/?id=3468099521
https://steamcommunity.com/sharedfiles/filedetails/?id=3468099387

Blue: The empty boxes both have true statements.
White: The blue box has a true statement.
Black: This box contains the gems.

Possible non-contradictionary true/value combinations:
T F F: invalid, blue and white are both true or both false
F T F: invalid, blue and white are both true or both false
F F T: invalid, blue and white are empty and thus both true
T T F: invalid, if blue and white are empty, black contains the gems and is thus true
F T T: invalid, white and blue are both true or both false
T F T: invalid, white and blue are both true or both false

As far as I can tell, there are no valid answers at all here.

The answer is FFT.

In this case, the white and blue box are both false. So the statement "The empty boxes both have true statements." on the blue box is false.

And the false form of "The empty boxes both have true statements" is "At least one of the empty boxes doesn't have a true statement" , which is true.

[Bayreuth]

∃A∃B(TrueBox(A)∧TrueBox(B)∧Empty(A)∧Empty(B)) or (∃A∃B(TrueBox(A)∧TrueBox(B)))→(Empty(A)∧Empty(B)) ？