Question 1
I 1 (USA 4), IMO1
Alice, Betty, and Carol took the same series of examinations. There was one grade of $A$, one grade of $B$, and one grade of $C$ for each examination, where $A,B,C$ are different positive integers. The final test scores were
$$\begin{array}{ccc}\text{Alice}&\text{Betty}&\text{Carol}\\20&10&9\end{array}$$
If Betty placed first in the arithmetic examination, who placed second in the spelling examination?
Alice, Betty, and Carol took the same series of examinations. There was one grade of $A$, one grade of $B$, and one grade of $C$ for each examination, where $A,B,C$ are different positive integers. The final test scores were
$$\begin{array}{ccc}\text{Alice}&\text{Betty}&\text{Carol}\\20&10&9\end{array}$$
If Betty placed first in the arithmetic examination, who placed second in the spelling examination?