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S _ D _ Clue
HE WOULD NEED TO PLACE THE 3-POUND WEIGHT AND THE 1-POUND WEIGHT ON THE SAME SIDE AS THE OBJECT AND BALANCE IT WITH THE 9-POUND WEIGHT. IF THE 2 GROUPS WEIGH THE SAME, THEN THE WEIGHT OF THE OBJECT IS 5 POUNDS. WHEN YOU PLACE A WEIGHT ON THE SAME PAN OF THE SCALE AS THE OBJECT YOU ARE WEIGHING, YOU SUBTRACT THAT WEIGHT FROM THE TOTAL OF THE WEIGHTS ON THE PAN ON THE OTHER SIDE THE MINIMUM NUMBER OF WEIGHTS REQUIRED IS FIVE AND THESE SHOULD WEIGHT 1, 3, 9, 27 AND 81 POUNDS. THE MERCHANT HAS TO USE A BALANCE WEIGHING SCALE TO DO THE JOB. TO WEIGH 2 POUNDS, HE'LL HAVE TO PUT THE 3 POUND WEIGHT ON ONE PAN AND 1 POUND WEIGHT ON THE OTHER PAN. TO WEIGH 5 POUNDS, HE'LL HAVE TO PUT THE 9 POUND WEIGHT ON ONE PAN AND 1 AND 3 POUND WEIGHTS ON THE OTHER PAN THE FOUR WEIGHTS ARE: 1, 3, 9 AND 17. THE FOURTH WEIGHT IS NOT 27 BECAUSE BY USING A 27 POUND WEIGHT, WE WOULD ABLE TO MEASURE UP TO 40 POUNDS. BUT SINCE WE NEED TO MEASURE ONLY UP TO 30 POUNDS, WE CAN SUBTRACT 10 FROM 27 TO GET 17. LET A=1, B=3, C=9 AND D=17. 1LBS = A 2LBS + A = B 3LBS = C 4LBS = A + B 5LBS + A + B = C 6LBS + B = C 7LBS + B = A + C 8LBS + A = C 9LBS = C 10LBS = A + C ... 20LBS = B + D ... 30LBS = A + B + C + D SPLIT THE PILLS INTO 3 GROUPS - 2 GROUPS WITH 3 PILLS EACH AND 1 GROUP WITH 2 PILLS. NOW PUT THE 2 GROUPS OF 3 PILLS ON THE SCALE. SCENARIO #1: BOTH GROUPS WEIGH THE SAME. THIS MEANS THAT THE POISONOUS PILL IS IN THE GROUP WITH 2 PILLS. SO TAKE THE 2 PILLS FROM THAT GROUP AND USE THE SCALE TO DETERMINE THE POISONOUS PILL. SCENARIO #2: ONE GROUP WEIGHS MORE THAN THE OTHER. TAKE ANY 2 PILLS FROM THIS GROUP OF 3 PILLS. IF THEY WEIGH THE SAME, THEN THE 3RD PILL IS THE POISONOUS PILL. IF THEY DON'T WEIGH THE SAME, THEN THE HEAVIER ONE IS OBVIOUSLY THE POISONOUS PILL