Question

One company has 700 employees. Prove there are at least two employees that have the same initials.

Answer 1

Answer:

You can choose the first letter of their initial 26 ways. And for each

of those ways, you can choose their other initial in 26 ways also. So

there are 26×26 or 676 different two-letter initials. Since there are

more than 676 employees in the company, there aren't enough different initials

to go around, so some employees must have the same initial.

[In any group of more than 366 people, there are bound to be some people with

the same birthday.]

[In a city of more than 26³ or 17,576 population, there are bound to be

residents with the same three-letter initials.]