17

Part of 2014 BMT Spring

Problems(2)

2014 BMT Team 17

Source:

Suppose you started at the origin on the number line in a coin-flipping game. Every time you flip a heads, you move forward one step, otherwise you move back one step. However, there are walls at positions

8

-8

; if you are at these positions and your coin flip dictates that you should move past them, instead you must stay. What is the expected number of coin flips needed to have visited both walls?

BMT 2014 Spring - Individual 17

Source:

A convex solid is formed in four-dimensional Euclidean space with vertices at the

24

possible permutations of

\{1, 2, 3, 4\}

(1, 2, 3, 4)

(1, 2, 4, 3)

, etc.). What is the product of the number of faces and edges of this solid?

combinatoricsgeometry