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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 SPLIT THE MARBLES INTO 3 GROUPS WITH 4 MARBLES EACH. PICK 2 GROUPS AND USE THE SCALE TO DETERMINE WHICH GROUP CONTAINS THE HEAVIER MARBLE. IF THE 2 GROUPS WEIGH THE SAME, THE HEAVIER MARBLE IS IN THE 3RD GROUP. ONCE THE GROUP IS DETERMINED, SPLIT THE MARBLES INTO 2 GROUPS WITH 2 MARBLES EACH. USE THE SCALE TO DETERMINE THE GROUP THAT CONTAINS THE HEAVIER MARBLE. LASTLY, USE THE SCALE TO WEIGH THE 2 REMAINING MARBLES TO DETERMINE THE HEAVIER MARBLE 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