Require x of y possible passwords to decrypt
This is a well studied problem in cryptography; what you're looking for is known as a Secret Sharing Scheme.  This is a scheme where we take a master secret, and from that generate $N$ shares, and with any collection of $T$ shares, we can reconstruct the master secret (and we can't with $T-1$ of them).  We can make $N$ and $T$ as large as we like, and so it works in the "any 218 out of 435" case.

See this article for more details, as well as pointers to practical ways to implement it.