CUNY Math Challenge: Could You Pass the Test?
Online, they grappled with challenging questions of probability, prime numbers, positive integers and Martian.... invasions. But the 164 students weren't playing computer fantasy games. They were competing in the second annual CUNY Math Challenge, designed to encourage the University's best undergraduate math talent -- and reward winners with cash prizes ranging from $500 to $2,500. After four qualifying rounds plus a seven-question, in-person final exam, Brooklyn College math major Stan Kats emerged as the grand prize winner. Kats, a junior, coaches the New York City Math Team and taught at the CCNY Summer Scholars program. Match Wits with the Winners!
Here's a question from the third qualifying round of the Math Challenge, which was established by the Office of Academic Affairs and the CUNY Institute for Software Design and Development. AS PART OF ITS PLAN to conquer the Earth (and to give college credit along the way), Mars selects a group of 23 students from a 100-level course in Practical Interplanetary Warfare to go to Earth. The Martian students (all of whom love math, naturally) agree to sit down and talk with 23 CUNY students, one from each CUNY institution. While the CUNY students are being briefed by the president and other world leaders, a conference seating plan has to be organized. The 46 delegates will sit around a round table.
The Martian lead professor insists that no Martian student can safely sit between two CUNY students. She also thinks that it would be dangerous to allow three CUNY students to sit as a group with no Martians in between. Can you devise a seating plan that will satisfy the Martian professor?
Either give a seating plan or prove that none is possible.