There is no actual way of "destroying coins". Even sending to an address with a private key that isn't known, a person can also get a lot (and i mean a real lot) amount of hashpower to bruteforce the key. Although it would be difficult, the coins are still recoverable.
Coins can be mined out of existence (miner selects a reward less than the max allowed).
Still coins sent to addresses with no known private key are effectively lost. No you can't brute force it with a lot of hashing power (not even all the computing power on the planet). If you could then Bitcoin would be worthless.