7.4. There are ten coins of different weights and a balance scale without weights. It is required to select the heaviest and the lightest coin. Can this be achieved in 13 weighings?
Answer: It is possible. Solution. First, divide all the coins into 5 pairs and in 5 weighings compare the weight of each pair. By selecting the heavier coin in each pair, we form a "heavy" group of 5 coins. The remaining 5 coins will form the "light" group. Now, in the heavy group, over 4 sequential weighings, select the heaviest coin. Similarly, in the light group, over 4 weighings, select the lightest coin. In total, $5+4+4=13$ weighings have been conducted.