After round one, she may have $0$ point, $1$ point, $2$points  After two rounds, she may have $3$, $4$, $6$, $7$, $8$ points 
Susan participates a Math competition. In round one, she needs to solve $2$ problems. If she works out one problem successfully, she will get $1$ point. Otherwise, she will not lose any points. In round two, she also needs to solve $2$ problems. If she works out one problem successfully, she will get $3$ points. Otherwise, she will lose $1$ point. Which number of points is it impossible for her to have？ 
Options:
[a] $$1$$ 
[b] $$3$$ 
[c] $$4$$ 
[d] $$6$$ 
[e] $$7$$ 