2015
Problem - 2003
Meena writes the numbers $1$, $2$, $3$, and $4$ in some order on a blackboard, such that she cannot swap two numbers and obtain the sequence $1$, $2$, $3$, $4$. How many sequences could she have written?
There are totally $4!=24$ ways to arrange these four numbers in a sequence. Among them, there are $C_4^2=6$ ways to make a sequence which can be constructed by switching two numbers. Therefore the answer to the original question is $24-6=\boxed{18}$.