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Combinatorics

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Same Initials

COMBIN-EAKIQX

In a directory of names (in the form first name, last name) what is the smallest number of people that would guarantee that there is a pair of people whose first names begin with the same letter and whose last names begin with same letter?

A

$26$

B

$27$

C

$28$

D

$676$

E

$677$

F

$1000$