Suppose we had 18 students working on various projects each month.

i. In January, there were 5 projects available. At least how many students are guaranteed to work on the same project?

ii. In February, you learned at least 2 students worked on the same project. At most how many projects were available that month?

iii. You overhear someone mention the following " Remember when there were 516 students! They had 86 projects together and capped the number of students on a project at 6 students per project. Every project still had at least 4 students! Talk about crazy!" Use what you have learned about the Pigeonhole Principle to explain why this scenario is possible.