SOLUTION TO PUZZLE 8:WEIGHT MACHINE PUZZLE

Solution to puzzle 8:weight machine puzzle

for question see here:weight machine puzzle

I measure 1kg with 1 and instead of choose 2 i pick 3.so now i can measure 2kg by placing 1 along with 2 in one side and 3 in another side.I can measure 4kg by placing 1,3 on one side and 4 on another side.

Now to measure   5kg intead of picking 5,pick the maximum number like a-4=5,a=9

S o now you can measure upto 13kg (eg:5=9-4,6=9-3,...12=9+3,13=9+4)
 To measure 14 pick b-14=13 which gives b= 27.Now you can measure upto 40kg.To measure 41kg pick b-41=40 which gives b=81


 so series is like 3^0,3^1,3^2,...
Since weights are within 1000kg minimum number of weights you can pick is 7.which are 1,3,9,27,81,242,729.

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