Let's say Alice wants to talk securely to Bob over the internet, and Eve is not only eavesdropping, but has managed to get into a MITM position.
In this scheme Alice and Bob exchange $n$ (example $n = 2$) plaintext questions, at least one for both parties (these are toy example questions):
Alice, what brand of car did I ride you to the airport with last December?
Bob, what's the serial number of the flashlight I gave you yesterday?
Is it then secure for Alice and Bob to attempt to use authenticated encryption under key $H(A_1 || \dots ||\ A_n ||\ S)$ where $A_n$ is the answer to the $n$th question (both parties will include the answers to their own questions), $S$ is a cryptographically strong salt, and $H$ is a slow key derivation function like scrypt?
This will only work if the answers are the exact same, so let's assume the answers have exact unambiguous answers.
Then, using this (seemingly temporarily secure) authenticated channel, can Alice and Bob exchange long-term proper crypto authentication certificates to foil Eve's future attempts at MITM?
Obviously, security can only be as good as the quality of the questions, so let's assume that Eve does not know the answer to any of the questions until the long-term exchange has completed, but we must assume Eve will be able to figure out the answers at a later time.