Jeff

Blue: Both of these statements are true. The gems are in this box.

White: The gems are not in the blue box. The gems are not in the black box.

Black: The gems are in a box with a false statement. Both statements on the blue box are true.

A: white

I guessed blue but was wrong.

Blue: The statements on this box are either both true or both false. This box is empty.

White: This box is white.

Black: All statements on the blue box are true. The box with no false statements has the gems.

A: Black

Blue: The gems are not in the black box.

White: This statement is as true as the statement on the black box.

Black: The gems are in the white box.

A: White

Blue: This is not an empty box. The gems are not in the black box.

White: This statement is true. The above statement is false.

Black: The gems are in the black box. The gems are in the white box.

A: Blue

Blue: The top statement on the white box is true. The gems are not in this box.

White: exactly two statements with the word 'true' are false. The gems are not in this box.

Black: both statements on the white box are true. Both statements on this box are true.

A: white

Blue: The black box is true and it contains the gems.

White: The black box is false. The above statement is false.

Black: The blue box is empty if it is false.

Answer: White

Blue: The white box has a true statement. The black box has a true statement.

White: The black box has a false statement. The gems are not in the box with two false statements.

Black: The blue box has two false statements. The box with two true statements has the gems.

Answer: Blue

Blue: The letter 'B' appears twice on the box that contains the gems.

White: All statements that contain more than one 'B' are true.

Black: The blue box contains gems.

Answer: Black

Blue: Only one statement is true.

White: A box next to this is true.

Black: A box next to this contains gems.

Answer: White

Blue: Only one of the statements on this box are false. The gems are in the white box.

White: Only one of the statements on this box are true. The gems are in a box with a true statement.

Black: There are three false statements on boxes in this room.

Answer: Blue

I guessed black but was wrong.

Blue: "Statements containing the word 'statements' are always true."

White: "Both statements on the black box are false."

Black: "The gems are in the box with a true statement. This is the second statement on this box."

A: Black

Blue: "The gems are in a box with the longest word. 'Longest' is the longest word on a box.

White: "The gems are in a box with the shortest word. 'A' is the shortest word on a box.

Black: There are words on the box with the gems. This box does not contain the gems."

A:???

I guessed white but was wrong

Blue: "Only one box next to this box is false and it contains gems."

White: "Only one box next to this box is false and it contains gems."

Black: "Only one box next to this box is false and it contains gems."

A: White

Blue: "The white box has exactly one true statement. The black box has no true statements."

White: "The gems are not in the black box. The above statement is true."

Black: "The blue box has exactly one true statement. The gems are in the blue box."

A: Blue

Blue: "There is only one true box."

White: "Both statements written on the other boxes are false."

Black: "The box with the most words does not have gems."

A: Black

Blue: "The second statement on the black box is false. The black box contains the gems."

White: "Every statement with the word 'blue' is false."

Black: "Both statements on the blue box are true. The blue box contains gems."

A: Black

Blue: "The gems are not in this box. The gems are not in the white box."

White: "The gems are not in this box. The gems are in the blue box."

Black: "The gems are not in this box. The gems are in the blue box."

A: Black box

I guessed blue but was wrong, can't be white because every box would have at least one false statement statement, so black must contain them, which also satisfies the at least one box with all true statements and at least one box with all false statements (in this case blue is all true, black is all false, and white is partial).

Blue box: "You will open this box and find it empty"

White box: "A true box contains the gems"

Black box: "This box and the white box are both false"

A: White box

Blue box: "You will not solve this puzzle"

White box: "Four statements on boxes in this room are true. A box with one false statement contains gems."

Black box: "A box with a true statement contains the gems. This box does not contain the gems."

A: white

I guessed black but was wrong.