First of all, no additional information was needed.
Secondly you are implicitly assuming a probability distribution on the numbers in the envelopes, namely that it is evenly distributed among all possible numbers that could be written on the pieces of paper. This assumption is both wrong and unnecessary.
Thirdly note that the technique must work no matter what pair of numbers happen to be in the envelope. Creating a technique which will work for 90% of the pairs that you think could be there won't cut it. It has to be all pairs.