You have four coins to sort with a standard balance scale. Their weights are 20g, 21g, 22g and 23g. Prove that there is no strategy which can guarantee sorting the coins with only three weighings.
(In reply to re: Information theory way
There is only one grouping (A with D and B with C) which produces an equal weighing. If you used this weighing in your results, you would only use it once. Thus, in every group of 3 (rational) weighings, equal only will appear once, showing that you can only get at most 12 different results.
Posted by Gamer
on 2007-03-09 11:43:25