Thinking Cap

Problem of the Month


Congratulations to Ryan Chimienti, winner of the September 2019 Problem of the Month competition!

October 2019

On the job market

There are 20 businesses in Norman, each of which is looking to hire 15 new employees. A group of 300 OU students is interviewed by each one of the 20 businesses. Each business rates each student as qualified or unqualified to work for them, in such a way that each business finds exactly \(q\) students to be qualified, and each student is considered to be qualified by at least one business.

Find the smallest value of \(q\) for which it is always possible to assign 15 students to each business, in such a way that each business gets assigned only students they consider to be qualified, and each of the 300 students gets assigned to a business.