11. A lot of snow fell, and the children decided to build snowmen. For this, they rolled 99 snowballs with masses of 1 kg, 2 kg, 3 kg, ..., 99 kg. A snowman consists of three snowballs stacked on top of each other, and one snowball can be placed on another if and only if the mass of the first is at least twice as small as the mass of the second. What is the maximum number of snowmen the children can build?
11. Answer: 24.

Two snowballs with masses from 50 to 99 kg cannot end up in the same snowman, so in each snowman, there will be at least two snowballs with masses from 1 to 49 kg. Therefore, there cannot be more than 24 snowmen.

An example can be constructed greedily: first, take three snowballs with masses, for example, 96, 48, and 24 kg. Now, if the mass of each is reduced by 1, the snowman can still be formed. Indeed, if the larger snowball decreases by 1, then to maintain the inequality, the smaller one must decrease by at least 0.5, but it also decreases by 1.