LeetCode 416 Partition Equal Subset Sum - Problem Statement

Given an integer array $nums$, return true if you can partition it into two subsets with equal sums. For example, $[1, 5, 11, 5]$ can be split into $[1, 5, 5]$ and $[11]$, both summing to 11. At first glance, this looks nothing like knapsack. There's no weight limit, no values.

But here's the connection: if the total sum is $S$, you need to find a subset that sums to exactly $S/2$. That's subset sum. Before reading on, think about this: when is it impossible to partition? What condition on the total sum guarantees failure?