How to connect M from N?

Question

Algorithms

I do not know how to formulate the question correctly, or how it is called at least.
There are input parameters X , Y , Z. Is it possible to create an output fingerprint that will be equal to any M of N values, and from which these values ​​cannot be identified.
Where M and N can be

2 из 3
3 из 3
3 из 4
4 из 4
3 из 5
4 из 5
5 из 5

As an example

X:5
Y:6  => ABC
Z:7

Fn(X, Y) = ABC
Fn(X, Z) = ABC
Fn(Y, Z) = ABC
Fn(X, Y, Z) = ABC

Fn(X, Q) = FED

Answer 1

Let's take the 2 out of 3 option.
F(X, T, Z) = F(X, Y, Z) = F(X, Y, Q)
But
F(X, T, Z) ≠ F(X, Y, Q)
Therefore, such a function cannot exist .
The only thing you can do is to calculate the distance function
F((X, Y, Z), (X, T, Z)) = 1
F((X, Y, Z), (X, Y, Q)) = 1
F ((X, T, Z), (X, Y, Q)) = 2