Problem:
Three members of the Euclid Middle School girls' softball team had the following conversation.
Ashley: I just realized that our uniform numbers are all -digit primes.
Bethany: And the sum of your two uniform numbers is the date of my birthday earlier this month.
Caitlin: That's funny. The sum of your two uniform numbers is the date of my birthday later this month.
Ashley: And the sum of your two uniform numbers is today's date.
What number does Caitlin wear?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The sum of any two of the girls' uniform numbers must be no greater than . The only possible sums of two -digit primes that are no greater than are
Therefore the required dates are , and . Caitlin's uniform number must appear in the two smallest sums, and . So Caitlin's uniform number is . The other two girl's uniform numbers are for Ashley and for Bethany.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions