H _
W _ _ L D
N _ _ D
T _
P L _ C _
T H _
3 - P _ _ N D
W _ _ G H T
_ N D
T H _
1 - P _ _ N D
W _ _ G H T
_ N
T H _
S _ M _
S _ D _
_ S
T H _
_ B J _ C T
_ N D
B _ L _ N C _
_ T
W _ T H
T H _
9 - P _ _ N D
W _ _ G H T .
I F
T H _
2
G R _ _ P S
W _ _ G H
T H _
S _ M _ ,
T H _ N
T H _
W _ _ G H T
_ F
T H _
_ B J _ C T
_ S
5
P _ _ N D S .
W H _ N
Y _ _
P L _ C _
_
W _ _ G H T
_ N
T H _
S _ M _
P _ N
_ F
T H _
S C _ L _
_ S
T H _
_ B J _ C T
Y _ _
_ R _
W _ _ G H _ N G ,
Y _ _
S _ B T R _ C T
T H _ T
W _ _ G H T
F R _ M
T H _
T _ T _ L
_ F
T H _
W _ _ G H T S
_ N
T H _
P _ N
_ N
T H _
_ T H _ R
S _ D _ Clue
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 NUMBER THE BUCKETS 1 THROUGH 20. TAKE ONE BLOCK FROM BUCKET 1, TWO FROM BUCKET 2, THREE FROM BUCKET 3, AND SO ON, UNTIL YOU HAVE 20 BLOCKS FROM BUCKET 20. THEN STACK AND WEIGH THE 210 BLOCKS (1 + 2 + 3 + ... + 18 + 19 + 20 = 210). IF ALL THE BLOCKS WEIGH 16OZ EACH, THEN THE SCALE WOULD READ 3360OZ. HOWEVER, THE SCALE WILL ACTUALLY READ OVER THIS BY A NUMBER OF OUNCES THAT CORRESPONDS TO THE NUMBERED BUCKET WITH THE HEAVIER BLOCKS SINCE EACH HEAVY BLOCK ADDS 1 OUNCE. FOR EXAMPLE, IF THE HEAVIER BLOCKS ARE IN BUCKET 10, THE SCALE WOULD READ 3370OZ SINCE THERE ARE 10 BLOCKS THAT WEIGHT 17OZ EACH. SUBTRACTING THE WEIGHT ON THE SCALE WITH 3360OZ WILL GIVE THE BUCKET NUMBER: 3370 - 3360 = 10 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 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