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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 THE KING KEEPS POISON 12 SO THAT HE CAN NEUTRALIZE ANY POISON THAT THE CLOWN GIVES HIM. HE POURS POISON 10 (HIS SECOND STRONGEST POISON) AND GIVES IT TO THE CLOWN TO DRINK. CLOWN CAN DEDUCE THIS SO HE KEEPS POISON 11 FOR HIMSELF TO NEUTRALIZE POISON 10. THAT'S HOW HE SURVIVES. HE ALSO KNOWS THAT THE KING, AFTER DRINKING THE CUP HE GAVE HIM, WILL DRINK POISON 12 TO NEUTRALIZE THE POISON. SO THE CLOWN POURS PLAIN WATER INSTEAD OF POISON INTO THE CUP FOR THE KING. THE KING DRINKS THE WATER (WATER IS NOT POISON) AND RIGHT AFTER THAT HE DRINKS THE STRONGEST POISON POSSIBLE (12) AND DIES 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 FILL UP THE 3 GALLON CONTAINER AND POUR THE 3 GALLONS INTO THE 5 GALLON CONTAINER. THEN, FILL THE 3 GALLON CONTAINER BACK UP, AND POUR IT INTO THE 5 GALLON CONTAINER. THE 3 GALLON CONTAINER WILL HAVE 1 GALLON LEFT. EMPTY THE 5 GALLON CONTAINER. POUR THE REMINING 1 GALLON INTO THE 5 GALLON CONTAINER. THEN FILL THE 3 GALLON CONTAINER BACK UP AND POUR IT INTO THE 5 GALLON CONTAINER. THUS, YOU HAVE 4 GALLONS