Bob has developed a specialized data repository and has granted access to this repository

exclusively to a group, who are sequentially numbered from$1$ to $n.$ He has set a specific access

rule: the person with the ID number $"i"$ is permitted to access the repository up to $"i"$ times.

Bob has implemented a visitation tracking system. This system includes a counter, $"$K$",$ which

records the total number of accesses to the repository. However, it does not reveal the

identity of the person accessing it$.$ Your task is to analyze this scenario and determine a

critical value for $"K".$

Question:

What is the minimum value of $"$K$"$ at which Bob can be certain that at least one person has

reached their maximum number of permitted repository visits? Don't need to build a program for

your answer. A detailed explanation with examplesis enough.