least 677 people must be in the school.
are 26 letters
in the English alphabet. So there are 26
different possibilities for
the first initial. Consider all the possible
pairs of two initials.
suppose a person has the first initial A. Then the pair
of initials could be AA, AB, AC, ., AZ. There are 26 different
possibilities. If the first initial is B, the pair of
initials could be BA, BB, BC, ., BZ. Again
there are 26 different pairs.
in this way and since there are 26 possible first initials,
each of which could be paired with 26 last initials, there
are 26 ×
26, or 676 possible different pairs of initials.
If there were 677 people, at least two of them must have
the same pair of initials.