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C _ N T _ _ N _ R Clue
BASED ON THE RIDDLE, WE CAN COME UP WITH THE FOLLOWING EQUATION: X/6 + X/12 + X/7 + 5 + X/2 + 4 = X WHERE X IS DIOPHANTUS'S AGE AT THE TIME OF HIS DEATH. SOLVING FOR X GIVES A VALUE OF 84 FILL THE 5 OZ. AND 11 OZ. CONTAINERS FROM THE 24 OZ. CONTAINER. THIS LEAVES 8 OZ. IN THE 24 OZ. BOTTLE. NEXT EMPTY THE 11 OZ. BOTTLE BY POURING THE CONTENTS INTO THE 13 OZ. BOTTLE. FILL THE 13 OZ. BOTTLE FROM THE 5 OZ. CONTAINER (WITH 2 OZ.) AND PUT THE REMAINING 3 OZ. IN THE 11 OZ. BOTTLE. THIS LEAVES THE 5 OZ. CONTAINER EMPTY. NOW POUR 5 OZ. FROM THE 13 OZ. BOTTLE INTO THE 5 OZ. BOTTLE LEAVING 8 OZ. IN THE 13 OZ. BOTTLE. FINALLY POUR THE 5 OZ. BOTTLE CONTENTS INTO THE 11 OZ. BOTTLE GIVING 8 OZ. IN THIS CONTAINER THE CHILDREN ARE 1, 6 AND 6 YEARS OLD. THE PRODUCT OF THEIR AGES IS 36, SO NONE OF THEM CAN BE OLDER THAN 36. THE NUMBER 36 HAS TO BE EXPRESSED AS THE PRODUCT OF 3 NUMBERS. THEIR POSSIBLE AGES ARE (THE SUM OF THEIR AGES IS IN BRACKETS): 1, 1, 36 (3938) 1, 2, 18 (21) 1, 3, 12 (16) 1, 4, 9 (14) 1, 6, 6 (13) 2, 2, 9 (13) 2, 3, 6 (11) 3, 3, 4 (10) SINCE CHERYL IS TOM'S NEXT DOOR NEIGHBOUR, TOM KNOWS CHERYL'S HOUSE NUMBER. TOM WOULD KNOW THE CHILDREN'S AGES IN EVERY CASE THAT SUMS UP TO A UNIQUE NUMBER EXCEPT FOR THE SUM OF 13, WHICH HAVE 2 COMBINATIONS OF POSSIBLE AGES. AS A RESULT, TOM WOULD BE CONFUSED AS HE HAS TO PICK BETWEEN THE 2 COMBINATIONS: (1,6,6) AND (2,2,9). CHERYL THEN TELLS TOM ABOUT HER YOUNGEST CHILD WHO LIKES STRAWBERRY MILK WHICH TELLS TOM THAT THERE IS ONLY 1 YOUNGEST CHILD NO. THIS IS A SITUATION WHERE YOU LOSE EVEN IF YOU WIN. ASSUMING THE OTHER PERSON IS BEING WISE, THEY WOULD TAKE YOUR $2 AND SAY, "I LOSE", AND GIVE YOU $1 IN RETURN. YOU WIN THE BET, BUT YOU'RE OUT $1