Discussion 6

Page 90 Question 16

Prove that at least two people in Atlanta, Georgia have the same initials, assuming no one has more than four initials.

#Number of people in Atlanta, Georgia
num_in_atlanta = 496000

# Number of possible combinations of initials for 4 initials or less
twoInitials = 26 * 26
threeInitials = 26 * 26 * 26
fourInitials = 26 * 26 * 26 * 26

total = twoInitials + threeInitials + fourInitials

print(total)

## [1] 475228

num_in_atlanta - total

## [1] 20772

Answer: There are over 496,000 people in Atlanta, Georgia. The number of possible combinations of initials for people with two, three, or four initials is 475,228 combinations. Since this number is less than the number of people, at least two people will have the same initials. If 475,228 people have all different initials, then the rest of the 20,772 people living in Atlanta must have the same initials as other people.