Solution to Math Challenge Problem

No seating plan can be made.

Suppose a seating plan could be made with the delegates arranged in the order d1, d2, d3, ... d46 around the table. Imagine reseating the delegates around 2 smaller tables, the first holding the odd numbered delegates in the order d1, d3, d5, ... d45 and the second holding the even numbered delegates in the order d2, d4, d6...d46. On the small table for odd numbered delegates, no two adjacent places can be occupied by CUNY students (otherwise at the big table, those two CUNY students would have to either be on each side of a Martian, which is not allowed, or be on either side of a third CUNY student to form an illegal group of 3 CUNY students).

This means that at least half the delegates in odd positions are Martians. That is, there are at least 12 Martians in odd numbered positions.

Exactly the same reasoning shows that at least 12 Martians have even numbered positions -- and this would require at least 24 Martian delegates, a contradiction.