Which box has the gems[spoiler]?

[󠀡󠀡vainquit]

blue：one of the other statements is false
white: one of the other boxs contains gems
black: if you replace the word "one" in the other two statements with "both", they will both false

I know the black is true. But what about the others?

[Superking]

As stated Black is True.

Suppose Blue is True. This would mean that White is False (both because of Blue's statement and because of the standard rules of the boxes), meaning that the gems are in White.

[Aris]

There's one trick for many of the box puzzles like this one: you know the puzzle must be solvable (knowing where the gems are), and only one statement here is relevant to gems. If white was true, you wouldn't know where the gems are and the puzzle would be unsolvable, so gems must be in white. This is generally easier than trying to solve it the "normal" way.

[󠀡󠀡vainquit]

Originally posted by Superking:

As stated Black is True.

Suppose Blue is True. This would mean that White is False (both because of Blue's statement and because of the standard rules of the boxes), meaning that the gems are in White.

It seems I've heard this before: Assuming a statement is true and then deriving a non-contradictory conclusion does not necessarily mean the statement is true; only when the assumption leads to a contradictory result can it prove that the assumption is false (so called "proof by contradiction").

[󠀡󠀡vainquit]

Originally posted by Aris:

There's one trick for many of the box puzzles like this one: you know the puzzle must be solvable (knowing where the gems are), and only one statement here is relevant to gems. If white was true, you wouldn't know where the gems are and the puzzle would be unsolvable, so gems must be in white. This is generally easier than trying to solve it the "normal" way.

Wow!!That's really a smart solution!

[Superking]

Originally posted by 󠀡󠀡vainquit:

It seems I've heard this before: Assuming a statement is true and then deriving a non-contradictory conclusion does not necessarily mean the statement is true; only when the assumption leads to a contradictory result can it prove that the assumption is false (so called "proof by contradiction").

For the box puzzles in the game we have an additional piece of knowledge, namely that there is only one solution, This means that if we find a valid set of true/false values for the statements it has to be the answer.

[󠀡󠀡vainquit]

Originally posted by Superking:

Originally posted by 󠀡󠀡vainquit:

It seems I've heard this before: Assuming a statement is true and then deriving a non-contradictory conclusion does not necessarily mean the statement is true; only when the assumption leads to a contradictory result can it prove that the assumption is false (so called "proof by contradiction").

For the box puzzles in the game we have the additional piece of knowledge, namely that there is only one solution, This means that if we find a valid set of true/false values for the statements it has to be the answer.

That makes sense! I'll check this later