Partitioning a set to the maximum number of subsets summing to zero
3-Partition reduces to this problem, so it's strongly $NP$-hard. Moreover, 4-Partition also reduces to it (and the blowup is linear), so assuming the exponential time hypothesis there's no $2^{o(n)}$ algorithm.

Using dynamic programming there's a $O^*(4^n)$ algorithm, it would be interesting if you could do $2^n$ or even $1.99^n$.