Toasty’s Problem Stash

I like writing math problems! Whenever I feel like it, I’m going to add a new problem I’ve written here.

(2/7/2026) Let an ordered tuple of non-negative real numbers $(a_1, \ldots, a_{2026})$ be chosen uniformly at random. Given that $a_1 + \cdots + a_{2026} = 1$, what is the probability that $a_i \leq \tfrac{1}{2}$ for all $1 \leq i \leq 2026$?

(10/1/2022) Let quadrilateral $ABCD$ be inscribed in a circle. Let the line through $B$ perpendicular to $AC$ intersect on side $AD$ at a point $E$. If $AE=BE=DE=5$ and $AB=6$, what is $CD$?

For more problems written by me, check out Toasty’s Problems!