Below is an initial state for Conway's Game of Life with a single pulsar. Living cells are white.
The area marked with red is your base. You are free to modify any of the red cells, but only those, and only in the initial generation. You are not allowed to do anything once the simulation starts.
Your goal is to annihilate every living cell in the grid – in other words, the game must reach a generation where every cell is dead, even in your base. Yet in other, way cooler words:
You have to construct a rocket to destroy the Sun and everything that was created in the process.
The grid is infinite in every direction, i. e. runaway gliders still count as living.
You may use a brute force algorithm if you really wish, but I don't recommend you to. For one thing, you're up against the halting problem. Besides, finding a good construction all by yourself is fun (at least it was for me).
What I do recommend is downloading a good GoL simulator – solving this with only a paper and a pencil is probably not so much fun.
EDIT: The puzzle has been solved, but please don't be discouraged from posting alternative solutions. They are still very valuable, as they seem hard to come up with.