Computer Science
# Strings

$a$ and $b$. We want to devise a function $f(a,b)$ that tells us how close the two strings are. A reasonable measurement would be to measure how many "edits" operations have to be made to one string in order to change it to the other. There are three possible "edit" operations:

Suppose we are given two stringsSubstitution: Replacing a single character from $a$ so that it matches $b$ costs $1$. If $a=\text{rot}$ and $b=\text{dot}$. Then $f(a,b)=1$.

Insertion: Inserting a single character also costs $1$. Ie, If $a = \text{girl}$ and $b=\text{girls}$, then $f(a,b)=1$.

Deletion: Deleting a single character also costs $1$. Ie. If $a=\text{hour}$ and $b=\text{our}$ then $f(a,b)=1$.

Given $a$ and $b$, compute $f(a,b)$.

Let the **reverse** of a positive integer $n$, denoted $R(n),$ be the result when the digits of the number are written backwards; for example, $R(190) = 091,$ or just $91.$

Call a positive integer $n$ **brilliant** if $n + R(n)$

is a multiple of 13. Let $B$ be the $10000$th brilliant number. Compute the last three digits of $B.$

**PalPrime** is a prime number that is also a palindrome.The first few PalPrimes are $2, 3, 5, 7, 11, 101, 131, 151, 181, 191...$. Let $S$ be the sum of the digits of the largest PalPrime $N$ such that $N<10^9$.What is the value of $S$?