An interesting Putnam problem on the Pigeonhole Principle

The following problem is contained in the book “Putnam and Beyond” by Gelca, and I saw it on stackexchange. I’m mainly recording this solution because it took me longer than usual to come up with the solution, as I was led down the wrong path many a time. Noting what is sufficient for a blockContinue reading “An interesting Putnam problem on the Pigeonhole Principle”

Thinking about a notorious Putnam problem

Consider the following Putnam question from the 2018 exam: Consider a smooth function such that , and and . Prove that there exists a point and a positive integer such that . This is a problem from the 2018 Putnam, and only 10 students were able to solve it completely, making it the hardest questionContinue reading “Thinking about a notorious Putnam problem”