https://pgadey.ca/tags/problem-solving/ Recent content in Problem Solving on Parker Adey Hugo en-EN Wed, 10 Apr 2024 09:55:51 -0400 https://pgadey.ca/office-camera/2023-06-19t12c12c26-04c00/ Mon, 19 Jun 2023 12:12:26 -0400 https://pgadey.ca/office-camera/2023-06-19t12c12c26-04c00/ <p><img src="https://pgadey.ca/images/office-camera/2023-06-19T12:12:26-04:00.jpeg" alt="A photo of a whiteboard titled: Putnam B4 2005" title="Putnam B4 2005"></p> <p>For positive integers $m$ and $n$, let $f(m, n)$ denote the number of $n$-tuples $(x_1, x_2, \dots , x_n)$ of integers such that $|x_1|+|x_2|+ \cdots +|x_n| \leq m$. Show that $f(m, n) = f(n, m)$.</p>