The towns in one country are connected with bidirectional airlines, which are paid in at least one of the two directions. In a trip from town A to town B there are exactly 22 routes that are free. Find the least possible number of towns in the country. 
To solve this problem, we need to determine the minimum number of towns \( n \) such that there are exactly 22 free routes from town \( A \) to town \( B \). We will analyze the problem step-by-step.

1. **Initial Analysis for Small \( n \)**:
   - For \( n = 2 \), there is only 1 route from \( A \) to \( B \).
   - For \( n = 3 \), there are \( 3! = 6 \) routes from \( A \) to \( B \).
   - For \( n = 4 \), there are \( 4! = 24 \) routes from \( A \) to \( B \).
   - For \( n = 5 \), there are \( 5! = 120 \) routes from \( A \) to \( B \).

   Clearly, for \( n = 2, 3, 4, 5 \), the number of routes is either too small or too large compared to 22. Therefore, \( n \) must be greater than 5.

2. **Analysis for \( n = 6 \)**:
   - Consider the towns \( A, B, a_1, a_2, a_3, a_4 \).
   - We need to check if we can have exactly 22 free routes from \( A \) to \( B \).

   Let's denote the free routes as follows:
   - \( A \rightarrow a_i \) for \( i = 1, 2, 3, 4 \) (4 routes).
   - \( a_i \rightarrow B \) for \( i = 1, 2, 3, 4 \) (4 routes).
   - \( a_i \rightarrow a_j \) for \( i \neq j \) (12 routes).

   Total free routes: \( 4 + 4 + 12 = 20 \).

   Since 20 is less than 22, it is not possible to have exactly 22 free routes with \( n = 6 \).

3. **Analysis for \( n = 7 \)**:
   - Consider the towns \( A, B, a_1, a_2, a_3, a_4, a_5 \).
   - We need to check if we can have exactly 22 free routes from \( A \) to \( B \).

   Let's denote the free routes as follows:
   - \( A \rightarrow a_i \) for \( i = 1, 2, 3, 4, 5 \) (5 routes).
   - \( a_i \rightarrow B \) for \( i = 1, 3, 5 \) (3 routes).
   - \( a_i \rightarrow a_j \) for \( i < j \) (10 routes).

   Total free routes: \( 5 + 3 + 10 = 18 \).

   This is still less than 22. However, we can add more free routes between the intermediate towns to reach exactly 22.

   - Add \( a_1 \rightarrow a_2 \), \( a_2 \rightarrow a_3 \), \( a_3 \rightarrow a_4 \), and \( a_4 \rightarrow a_5 \) (4 additional routes).

   Total free routes: \( 18 + 4 = 22 \).

   Therefore, it is possible to have exactly 22 free routes with \( n = 7 \).

Conclusion:
The least possible number of towns in the country such that there are exactly 22 free routes from town \( A \) to town \( B \) is \( n = 7 \).

The final answer is \( \boxed{7} \).