View source for Northeastern WOOTers Mock AIME I Problems/Problem 8

== Problem == 
Dai the Luzon bleeding-heart has numbered lillypads, <math>1</math> through <math>100</math>. Then, Ryan the alligator eats those lillypads with the intention of eating Dai. Dai starts on a random lillypad and flies around between lillypads randomly every minute. Ryan also eats a random lillypad every minute. If the expected number of minutes left for Dai to live is <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers, find <math>m+n</math>.

== Solution ==


101/2 ---> 103