RSA: Given (e,c,d) is possible to solve? is it possible to solve RSA without n?

I know e, c and d
No, it would appear to be a hard problem; being able to recover the plaintext allows us to recover $n$ (at least, for small $e$), and recovering $n$ would appear to be difficult.

Knowing $e, d$, we know that $ed \equiv 1 \pmod{ \text{lcm}(p-1, q-1)}$, or equivalently, $ed - 1 = \frac{k}{\text{gcd}(p-1, q-1)} (p-1)(q-1)$, for some integer $k$.

As both $k$ and $\text{gcd}(p-1, q-1)$ are likely to be small (and from $c$, we can get a rough idea about the size of $n$), we are likely to be able to have a plausible guess to $(p-1)(q-1)$.

However, to convert that to $pq$, we'll need to factor $(p-1)(q-1)$; while $p-1, q-1$ both a likely to have some small factors (allowing us to reduce the size of the problem a bit), however, it appears likely that there won't be enough small factors to reduce the size enough; performing a complete factorization won't be all that much easier than the original 'factor $pq$' problem...