YATES: Kline knows the color of the Safe Room button but not the number. Nguyen knows the number but not the color.

KLINE: I don’t know which button it is. But I know Nguyen doesn’t know either.

NGUYEN: At first I didn’t know. But now I know which button it is.

Kline says he knows Nguyen doesn’t know the button. He can only be certain of this if the button isn’t red (if the color were red and the number were 4, Nguyen would immediately know Red 4). Once Kline makes this statement, Nguyen can deduce the button isn’t red. After red is ruled out, orange and green still share the same numbers, so the only way Nguyen can identify the button with certainty is if it’s Blue 1.

You enter the Safe Room.

Thank you for your compliance. Your safety is now the facility’s responsibility.