S T _ T _ M _ N T
3
_ S
C _ R R _ C T .
B _ X
A
C _ N T _ _ N S
T H _
B L _ _
C H _ P ,
B _ X
B
T H _
R _ D
C H _ P ,
_ N D
B _ X
C
T H _
W H _ T _
C H _ P .
I F
S T _ T _ M _ N T
1
_ S
C _ R R _ C T ,
T H _ N
S T _ T _ M _ N T
2
W _ L L
_ L S _
B _
C _ R R _ C T
( _ N D
V _ C _
V _ R S _ ) ,
S _
S T _ T _ M _ N T
3
H _ S
T _
B _
C _ R R _ C T Clue
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 THE ONE LABELED BOTH. SINCE YOU KNOW THAT THE BOX IS LABELED INCORRECTLY, IT MUST HAVE ALL BLACK MARBLES OR ALL WHITE MARBLES. IF A BLACK MARBLE COMES OUT, YOU KNOW THAT HAS TO BE THE BLACK MARBLES BOX, SO YOU PUT THE "BLACK" LABEL ON IT. THE BOX LABELLED "WHITE" MUST THEN BE LABELLED "BOTH" BECAUSE YOU KNOW IT IS ALSO LABELED INCORRECTLY, AND THEREFORE CAN'T BE WHITE. YOU WOULD LABEL THE LAST BOX "WHITE" BECAUSE THAT IS THE ONLY COLOR/BOX COMBO LEFT. IF THE FIRST MARBLE YOU PULLED OUT FROM THE BOX LABELED "BOTH" IS A WHITE MARBLE, THEN YOU SOLVE THE PROBLEM IN THE SAME GENERAL WAY STATEMENT 3 IS CORRECT. BOX A CONTAINS THE BLUE CHIP, BOX B THE RED CHIP, AND BOX C THE WHITE CHIP. IF STATEMENT 1 IS CORRECT, THEN STATEMENT 2 WILL ALSO BE CORRECT (AND VICE VERSA), SO STATEMENT 3 HAS TO BE CORRECT A MUST NOT HAVE SEEN TWO WHITE HATS ON B AND C, OR HE WOULD HAVE KNOWN HIS OWN HAT MUST BE BLACK SINCE THERE ARE ONLY TWO WHITE HATS. SO A'S ANSWER ESTABLISHES THAT AT LEAST ONE OF B OR C'S HAT IS BLACK. BASED ON A'S ANSWER, B KNOWS THAT HE AND C ARE EITHER BOTH WEARING BLACK, OR ONE IS WEARING BLACK AND ONE IS WEARING A WHITE HAT. IF B SEES THAT C IS WEARING A WHITE HAT, THEN HE WOULD KNOW HIS OWN HAT HAD TO BE BLACK. BUT B DOES NOT KNOW WHAT COLOR HAT HE IS WEARING, WHICH MEAN'S C'S HAT IS NOT WHITE AND MUST BE BLACK. SINCE BOTH A AND B CANNOT DEDUCE THE COLOR OF THEIR OWN HATS, C WILL KNOW THAT HE IS WEARING A BLACK HAT