Scenario Description:

Prof Karim has developed a specialized data repository and has granted access to this repository exclusively to a group of his CSI$2110$ students, who are sequentially numbered from $1$ to n$.$ He has set a specific access rule: the student with the ID number $$i$$ is permitted to

access the repository up to $$i$$ times.

Prof Karim has implemented a visitation tracking system. This system includes a counter, $$K$,$ which records the total number of accesses to the repository. However, it does not reveal the identity of the students accessing it$.$ Your task is to analyze this scenario and determine a critical value for $$K$.$

Question:

What is the minimum value of $$K$$ at which Le Prof can be certain that at least one student has reached their maximum number of permitted repository visits?

Note: you don$$t need to build a program for your answer. A detailed explanation with examples is enough.