Three members of the Euclid Middle School girls\textquotesingle~softball team had the following conversation.  Ashley: I just realized that our uniform numbers are all $$2-$$digit primes.  Bethany: And the sum of your two uniform numbers is the day of my birthday earlier this month.  Caitlin: That\textquotesingle s funny. The sum of your two uniform numbers is the day of my birthday later this month.  Ashley: And the sum of your two uniform numbers is today\textquotesingle s date.  What number does Caitlin wear?  ($$2014$$ AMC $$8$$ Problem, Question \#$$23$$) 
Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences
The maximum amount of days any given month can have is $$31$$, and the smallest, two-digit primes are $$11$$, $$13$$, and $$17$$. There are a few different sums that can be deduced from the following numbers, which are $$24, 30$$, and $$28$$, all of which represent the three days. Therefore, since Brittany says that the other two people\textquotesingle s uniform numbers add up to her birthday eadier in the month, that means Caitlin and Ashley\textquotesingle s numbers must add up to $$24$$. Similarly, Caitlin says that the other two people\textquotesingle s uniform numbers add up to her birhday later in the month, so the sum must add up to $$30$$. This leaves $$28$$ as today\textquotesingle s date. From this, Caitlin was referring to the uniform numbers $$13$$ and $$17$$ telling us that her number is $$11$$, giving our solution as $$(\text{A})=11$$. 