I have this problem of sharing a secret code $n\in\mathbb{Z}$ such that $0\le n\le250$ among five people.
There are 5 people, each one of whom receives a secret number $s_i$, $1\le i\le 5$ such that $0\le s_i \le 250$.
What is a good scheme that allows any 3 people to come together and recover the code, but any 2 people will have absolutely no idea of what the code is?
Any help will be greatly appreciated.
The problem you mention is called Secret Sharing. In general, Secret sharing is the problem of finding a set of keys to give to $n$ persons such that only sets containing $m$ people or more are able to decipher the thing. See the link for details (including possible algorithms such as Shamir's Secret Sharing).