All sets of 49 distinct positive integers less than or equal to 100 are considered. Leandro assigned each of these sets a positive integer less than or equal to 100. Prove that there is a set L of 50 distinct positive integers less than or equal to 100, such that for each number x of L the number that Leandro assigned to the set of 49 numbers L−{x} is different from x. Clarification: L−{x} denotes the set that results from removing the number x from L. combinatoricsnumber theory