Tímár Mihály found himself in a difficult situation because the red crescent fell off the bag where the treasure was hidden. All he knows is that the treasure is hidden in the heaviest of the four bags, buried in the wheat. It was revealed during three measurements that the first bag together with the second is lighter, together with the third is of the same weight, and together with the fourth is heavier than the other two bags. In which bag is the treasure?
Solution. Let the weights of the four bags be $A, B, C, D$ in the order given in the problem statement. According to the conditions of the problem:

$$
\begin{array}{ll}
\text { I. } & A+B<B+C \\
\text { II. } & A+C<C+D \\
\text { III. } & B+D<A+D
\end{array}
$$

By adding the corresponding sides of I. and III.: $C+D+A+D>A+B+B+C$, which means $D>B$.

By adding the corresponding sides of I. and II.: $A+B+A+C<B+C+A+C$, which means $D>C$.

Therefore, $D$ is the heaviest, so the treasure is in the fourth bag.