How many ships did the droplet destroy?
A single droplet destroyed almost the entire combined human fleet at the Doomsday Battle — roughly two thousand starships, wiped out in a matter of hours. Only a handful of ships survived, and none of them survived by fighting. They survived because they had already left the formation.
This is one of the most lopsided battles in all of science fiction: one half-ton probe against the assembled space military of two centuries of human civilization, and the probe never even slows down.
How big was the combined fleet?
The combined fleet numbered around 2,000 kilometer-scale warships, the merged main force of humanity's three great fleets. Every ship could accelerate to a significant fraction of light speed on its own. Humanity arranged all of them into a vast, almost ceremonial formation to "greet" the single approaching probe.
That formation turned out to be a mistake. Packed tightly together, the ships gave the droplet the shortest possible path from one target to the next. If you want the full roster and how this force was built, the history of the human space fleet lays out the timeline.
How did one droplet kill 2,000 ships?
The droplet attacks with nothing but itself. Its shell is made of strong-interaction material, a perfectly mirrored surface harder than anything humans can make. It simply rams each warship at high speed, punches straight through the fusion core, triggers the explosion, and flies out the other side undamaged to line up the next target.
Human armor and weapons are meaningless against it — you cannot scratch it, and it can pierce anything you have. The full mechanics and the sheer dread of that moment are broken down in the droplet attack scene and in the droplet's material and terror.
Which ships survived?
The only survivors were ships that were never in the battle formation. Before the fight, Zhang Beihai had already hijacked the starship Natural Selection and fled toward deep space at full burn — the moment captured in the Natural Selection hijacking. The fleet sent a small squadron to chase it, and that pursuit accidentally put those ships outside the droplet's kill radius.
Far from the Solar System, supplies running out, that squadron then fought humanity's first interstellar civil war. When it ended, just two ships sailed on into the dark: Blue Space and Bronze Age.
Did all ten droplets attack?
No. Trisolaris sent ten droplets, but only one carried out the Doomsday Battle. The other nine were blockading the Sun to suppress any dark forest broadcast. So one tenth of the droplet force was enough to erase 2,000 warships. Where the other nine went is traced in how many droplets Trisolaris sent.