### IMO Shortlist 2014 problem C6

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7. svibnja 2017.

We are given an infinite deck of cards, each with a real number on it. For every real number $x$, there is exacly one card in the deck that has $x$ written on it. Now two players draw disjoint sets $A$ and $B$ of $100$ cards each from this deck. We would like to define a rule that declares one of them a winner. This rule should satisfy the following conditions:

How many ways are there define such a rule? Here, we consider the rules as different if there exist two sets $A$ and $B$ such that $A$ beats $B$ according to the rule, but $B$ beats $A$ according to the other.

(Russia)

Izvor: https://www.imo-official.org/problems/IMO2014SL.pdf