/sci/ - Science & Math

PUZZLE:
You have a set S of 12 variables. Each is a real number. One variable has a value that is not equal to one; the other eleven variables all have a value of one.

You do not know which variable is the unusual one, nor do you know if it is greater or less than the others.

Define a function f: P -> R,
where P is the set of all subsets of S, and R is the set of real numbers. f(X) is the sum of all elements in X.

You have an oracle, which knows the value of each variable. However, you can only communicate with the oracle in the following way: You can present the oracle with two disjoint subsets of S, denoted X and Y, and the oracle will tell you which of the following is true:
f(X) > f(Y)
f(X) < f(Y)
f(X) = f(Y)

You may communicate with the oracle in this way three times. From this, you must deduce which variable has a unique value.

Note: This is entirely possible. If you try to prove that it is not, I will call you a troll.

Pic is broomrape.