Question 1
(USS) Three problems $A,B,C$ were given on a mathematics olympiad. All $25$ students solved at least one of these problems. The number of students who solved $B$ and not $A$ is twice the number of students who solved $C$ and not $A$. The number of students who solved only $A$ is greater by $1$ than the number of students who along with $A$ solved at least one other problem. Among the students who solved only one problem, half solved $A$. How many students solved only $B$?