This is a kind of task that's best solved by possibly spending more than the allocated 2 hours on it, once any obvious low-hanging fruit is picked. An optimization task is what a machine does best. So the real problem would be to construct a machine that would be able to run the optimization. A right optimization framework that results from the effort could also efficiently solve many more similar problems in the future.
I understand that this test is intended to somehow test the raw brianpower, the ability to tackle an unfamiliar and complicated domain, and to work under stress. But I hope it's not representative of the actual working conditions at Anthropic. It's like asking a candidate to play a Quake deathmatch when hiring to a special forces assault squad.