By the way, The answer to the broken weight problem was 1kg, 3kg, 9kg, and 27kg, Careful analysis will show that with a pair of scales and these weights you can establish any integer number of kgs of anything. e.g 25kg? put the 27kg and the 1kg on one side and the unknown weight and the 3kg on the other side - if they balance then you know that the unknown is 25kg. (both sides equal 28kg). The relationship between the fragments for this to work is increasing powers of three (three raised to the power of zero (1), three raised to the power of one (3), three squared (9) and three cubed(27)).