MathDB

Pieck the Frog hops on Pascal's Triangle, where she starts at the number

1

at the top. In a hop, Pieck can hop to one of the two numbers directly below the number she is currently on with equal probability. Given that the expected value of the number she is on after

7

hops is

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers, find

m+n

.
Proposed by Steven Yu

Problem Statement