Hey Hauguji ..good try... I rather solve it in a easier way. Using tristate logic... In binary there is 1 or 0. but in this trinary or tristate logic there are 3 stages ...-1( if the stone is in another pan) , 0 ( if the stone is not being used) and 1( if the stone is in the right pan while weighing) since there are 4 stones and 3 logic levels.. there are 3 to the power 4 states(3^4 = 81)..( similar to that of binary where 2^4 states if 4 bits are used) That gives us 81 states ... of which 40 are negative numbers(since there is -1 logic level), a zero and 40 positive numbers. These positive 40 numbers are the 40 states or 40 combinations. so now the weights of each stone ( similar to that of binary) wud be 3^0, 3^1, 3^2 and 3^3. Thus the weights are 1, 3, 9 and 27.