well, before i realised i had missed the sum part (which i suspect was added to foil lazy people like me) i would have argued that perhaps they are looking for someone who knows enough about the tools already available to find the fastest solution.
not that i have anything against the approaches here - the dynamic programming approach over trees is really cool and i probably wouldn't have thought of it myself. i just thought it amusing that there seemed to be a simpler way.
Ads are not the only model for providing free rides. Other Sustainable models exist:
Peer balancining: producers earn free credits for consumption. This is how Internet backbone peering and Team Fortress 2 work.
Freemium, or light users are too cheap to meter, while heavy users pay. This powered Zynga's IPO and many prosumer niches like Photography and web analytics.
Open core with professional services for customization or support (a mix of Freemium and free software). Cloudera.
How is Facebook different from telephone service, or USPS, or an ISP, under your analysis?
(Sidenote: USPS actually is ad-supported by bulk mail, and "heavy users subsidized" by parcel post. First class letter postage is really a nominal fee to eliminate DOS and DDOS attacks. )
All of those offered, at the time they appeared, a completely new service that had essentially zero competition, and have become entrenched since then (can you even e.g. get a job without a phone number?). Not to mention that the USPS is mandated by law to exist, so it can hardly be compared with Facebook.
Facebook never offered anything so revolutionary. It's just a well put together implementation of something that was already possible.
I can send a letter or a package to my grandma via USPS without her having to pay any subscription to USPS or "sign up" for USPS in any way.
Now, the early days of the telephone system might have been a better comparison to use in your argument than USPS. But I think it could be easily argued that the early telephone offered something much more unique for it's time than Facebook does.
When I read an article linked from Hacker News, then read some comments that are generally not tearing it to pieces, I assume the author must have some credibility and therefore is not throwing out conclusions for fun. Also, I have a minor in inferring existence of fascinating undetected evidence.
is even faster, but also missed the point.