11-8. In a caravan, there are 100 camels, both one-humped and two-humped, and there are at least one of each. If you take any 62 camels, they will have at least half of the total number of humps in the caravan. Let $N$ be the number of two-humped camels. How many values (in the range from 1 to 99) can $N$ take?
Answer: 72.

Solution. If there were $N$ two-humped camels in total, then there were $100-N$ one-humped camels, and there were $100+N$ humps in total. Let's line up the camels: first the one-humped ones, and then the two-humped ones. It is clear that if the condition for 62 camels is met for the first 62 camels, then it is met for any 62 camels. There are two possible cases: the first 62 camels are all one-humped, or there is at least one two-humped camel among them.

1) Suppose the first 62 camels are one-humped. Then, by the condition, $62 \geqslant \frac{1}{2}(100+N)$, from which $N \leqslant 24$.
2) Among the first 62 camels, there are two-humped ones, let their number be $y$. Then, by the condition, $62+y \geqslant \frac{1}{2}(100+38+y)$, from which $y \geqslant 14$. Then $N \geqslant 14+38=52$.

Thus, the number of two-humped camels lies in the ranges from 1 to 24 inclusive or from 52 to 99 inclusive. This gives $24+48=72$ options.