When a site asks you to set a password p$,$ they do not $($should not!$)$ store your password in plaintext. Instead

they store h$($p$),$ the hash of your password. Ideally, the function h is injective, but $$collisions$$ can occur. These happen when there are two distinct passwords p$1$ and p$2$ such that h$($p$1)=$ h$($p$2).$ Suppose the domain of h is all strings of $24$ lowercase english letters, and the codomain of h is all strings of $24$ hexadecimal digits. Under this scheme, prove that there must be at least one group of at least $100,000$ distinct passwords that all collide with each other.