Suppose you are consulting for a bank that is concerned about fraud detection, and they come to you with the following problem. They have a collection of n bank cards. Each bank card is a small plastic object, containing a smart chip with some encrypted data, and it corresponds to a unique account in the bank. Each bank can have many bank cards corresponding to it$,$ and we will say that two bank cards are equivalent if they correspond to the same account.

It is very difficult to read the account number off a bank card directly, but the bank has a high$-$ tech $$equivalence tester$$ that takes two bank cards and, after performing some computations, determines whether they are equivalent.

Their question is the following: among the collection of n cards, is there a set of more than n$/2$ of them that are all equivalent to one another? Assume that the only feasible operations you can do with the cards are to pick two of them and plug them into the equivalence tester