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T R _ _ Clue
YOU WILL HAVE TO SAY, "YOU WILL GIVE ME NEITHER COPPER NOR SILVER COIN." IF IT IS TRUE, THEN YOU WILL GET THE GOLD COIN. IF IT IS A LIE, THEN THE NEGATION MUST BE TRUE, SO THE STATEMENT BECOMES: "YOU WILL GIVE ME EITHER COPPER OR SILVER COIN". THIS WOULD BREAK THE GIVEN CONDITIONS THAT YOU GET NO COIN WHEN LYING. SO THE FIRST SENTENCE MUST BE TRUE PULL ONE COIN OUT OF THE CHEST MARKED "50 GOLD AND 50 SILVER COINS". IF IT'S A GOLD COIN, YOU KNOW THAT IT'S THE CHEST WITH 100 GOLD COINS. THE CHEST LABELLED "100 GOLD COINS" WILL THEN HAVE 100 SILVER COINS AND THE CHEST LABELLED "100 SILVER COINS" WILL HAVE 50 GOLD AND 50 SILVER COINS. IF THE FIRST COIN THAT YOU PULLED OUT FROM THE CHEST LABELLED "50 GOLD AND 50 SILVER COINS" IS A SILVER COIN, THEN YOU SOLVE THE PROBLEM IN THE SAME GENERAL WAY A HALF DOLLAR, A QUARTER, AND FOUR DIMES. YOU OBVIOUSLY CAN'T HAVE ANY PENNIES, BECAUSE YOU COULDN'T HAVE 1-4 PENNIES, SINCE $1.15 IS A MULTIPLE OF 5, AND IF YOU HAD 5 PENNIES OR MORE YOU COULD CHANGE A NICKEL. YOU CAN'T HAVE MORE THAN 1 NICKEL, OTHERWISE YOU COULD CHANGE A DIME. AND IF YOU HAD 1 NICKEL YOU COULDN'T HAVE BUT 1 DIME, OTHERWISE YOU COULD CHANGE A QUARTER. THEN IF YOU HAD 1 NICKEL AND 1 DIME YOU'D HAVE 15 CENTS. THAT WOULD LEAVE $1.00 AND YOU COULDN'T MAKE THAT REMAINING $1.00 WITH QUARTERS AND HALVES WITHOUT EITHER BEING ABLE TO CHANGE A HALF OR A DOLLAR. SO YOU CAN'T HAVE ANY PENNIES OR NICKELS. SINCE YOU CAN'T HAVE ANY PENNIES OR NICKELS, YOU CAN'T POSSIBLY MAKE $1.15 WITH DIMES AND HALVES ONLY, SO YOU MUST HAVE AT LEAST 1 QUARTER. YOU CAN'T HAVE MORE THAT ONE QUARTER, OTHERWISE YOU COULD CHANGE A HALF. SO YOU MUST HAVE EXACTLY 1 QUARTER. THAT LEAVES 90 CENTS, TO MAKE WITH A HALF DOLLAR AND DIMES. SO THAT'S 1 HALF AND 4 DIMES. AND WITH ONLY 4 DIMES YOU CAN'T CHANGE A HALF DOLLAR TAKE ONE COIN FROM THE FIRST BAG, TWO FROM THE SECOND, THREE FROM THE THIRD, AND SO ON, UNTIL YOU HAVE TEN COINS FROM THE TENTH. THEN STACK AND WEIGH THE 55 COINS (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10). SINCE EACH GOLD COIN WEIGH TEN GRAMS, IF ALL HAD BEEN GOLD, THE SCALE WOULD HAVE READ 550 GRAMS. THE AMOUNT BY WHICH THE WEIGHT WAS TOO LIGHT INDICATED THE NUMBER OF SILVER COINS AND THE NUMBER OF THE THE SILVER BAG. FOR INSTANCE, IF THE WEIGHT WAS 543 GRAMS, IT WOULD INDICATE THAT 7 SILVER COINS (550 - 543 = 7) HAD BEEN WEIGHED WITH THE GOLD COINS AND THAT THE REST OF THE SILVER COINS WERE IN THE SEVENTH BAG