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L _ B _ L _ D Clue
THE SILVER BOX CONTAINED ANNA'S PICTURE. IF HER PICTURE HAD BEEN IN THE GOLD BOX, THE STATEMENTS ON THE GOLD BOX AND SILVER BOX WOULD HAVE BEEN TRUE. IF HER PICTURE HAD BEEN IN THE BRONZE BOX, THE STATEMENTS ON THE BRONZE BOX AND SILVER BOX WOULD HAVE BEEN TRUE. IF HER PICTURE IS IN THE SILVER BOX, THE STATEMENT ON THE BRONZE BOX WOULD BE TRUE AND THE STATEMENTS ON THE GOLD AND SILVER BOXES WOULD NOT BE TRUE FIRST YOU SELECT A FRUIT FROM THE BOX MARKED PEACHES AND ORANGES. IF IT WAS A ORANGE YOU SELECTED, YOU KNOW THAT THE BOX COULD ONLY CONTAIN ORANGES. IF IT WAS A PEACH, YOU KNOW THAT THE BOX COULD ONLY CONTAIN PEACHES SINCE EACH BOX IS INCORRECTLY MARKED. IF, FOR EXAMPLE AN ORANGE WAS SELECTED, YOU WOULD MARK THAT BOX ORANGES AND SWITCH THE OTHER TWO INCORRECT LABELS AROUND. NOW ALL THREE WOULD BE CORRECTLY LABELED YOU WOULD ONLY NEED TO TAKE OUT ONE MARBLE BECAUSE WE KNOW THAT ALL OF THE LABELS ARE INCORRECT. SO YOU PULL ONE MARBLE OUT OF THE BOX LABELED "MIXED." IF RED COMES OUT, YOU KNOW THAT HAS TO BE THE ALL-RED BOX, SO YOU PUT THE RED LABEL ON IT. THE BOX LABELLED "BLUE" MUST THEN BE LABELLED "MIXED" BECAUSE YOU KNOW IT IS ALSO LABELED INCORRECTLY, AND THEREFORE CAN'T BE BLUE. YOU WOULD LABEL THE LAST BOX "BLUE" BECAUSE THAT IS THE ONLY COLOR/BOX COMBO LEFT. IF THE FIRST MARBLE YOU PULLED OUT FROM THE BOX LABELED "MIXED" IS A BLUE MARBLE, THEN YOU SOLVE THE PROBLEM IN THE SAME GENERAL WAY YOU WILL NEED TO OPEN A MINIMUM OF 2 BOXES. FIRST, OPEN THE BOX LABELLED APPLE; IF IT'S LABELLED CORRECTLY WE'RE DONE (THOUGH THIS IS PURELY BASED ON LUCK), OTHERWISE WE'LL FIND EITHER BANANAS, CARROTS, OR DATES. IN ANY OF THESE CASES, WE KNOW EITHER THAT THE BOXES LABELLED BANANAS, CARROTS, OR DATES MUST ALSO BE MISLABELED. IF THE FIRST OPENED BOX HAS: BANANAS INSIDE, THEN THE BOX LABELLED BANANA IS INCORRECT AND EITHER CARROTS OR DATES ARE CORRECT. CARROTS INSIDE, THEN THE BOX LABELLED CARROTS IS INCORRECT AND EITHER BANANA OR DATES ARE CORRECT DATES INSIDE, THEN THE BOX LABELLED DATES IS INCORRECT AND EITHER BANANA OR CARROTS ARE CORRECT. NO MATTER THE CIRCUMSTANCE, AFTER OPENING ONE BOX WE CAN IDENTIFY TWO REMAINING BOXES THAT MIGHT BE THE CORRECTLY LABELLED BOX. OPEN EITHER ONE OF THEM. IF IT'S THE CORRECTLY LABELLED BOX, WE'VE FOUND IT. OTHERWISE THE REMAINING UNOPENED BOX IS CORRECTLY LABELLED AND WE'VE FOUND IT. WE DON'T NEED TO OPEN IT TO DOUBLE CONFIRM