Category: teatime-puzzles

Hit the ball hard

Happy Wimbledon. Another teatime puzzle.

Let’s say we have a player with an extremely powerful but inconsistent serve. Half the time she aces, half the time she faults. What is the probability that she wins her service game?

Sean Eberhard current-events, teatime-puzzles 2 Comments 2021-06-292021-06-29

Weak subgroups

Here is a teatime puzzle.

Suppose ${G}$ is a finite group and ${S \subseteq G}$ is a subset containing the identity such that ${xy \in S}$ whenever ${x \in S}$ , ${y \in S}$ , and ${x \neq y}$ . Show that these are the only possibilities: