Ulamog, the Defiler

If Ulamog is entering the battlefield directly from exile, it will see itself when determining which card has the greatest mana value among cards in exile. If that's Ulamog, which seems likely, it will enter with ten +1/+1 counters on it.

Ulamog, the Defiler's first ability will resolve before Ulamog does. If Ulamog is countered or otherwise leaves the stack in response to its triggered ability, the triggered ability will still resolve as normal.

Use the number of +1/+1 counters on Ulamog at the time its annihilator ability resolves to determine how many permanents defending player should sacrifice.