I got the impression that it was more about mathematical sums being one of top items in von Neumann's mathematical toolkit, and he was really well-practiced in doing those. Then when he heard the puzzle he pattern-matched it to a problem he'd already solved enough times in his work to know it offhand, he didn't brute-force in his head 100x faster than other people who were rustier on sums and needed to brute-force things in their head.
