MathDB

The set of quadruples

(a,b,c,d)

where each of

a,b,c,d

is either

0

1

is called vertices of the four dimensional unit cube or 4-cube for short. Two vertices are called adjacent, if their respective quadruples differ by one variable only. Each two adjacent vertices are connected by an edge. A robot is moving through the edges of the 4-cube starting from

(0,0,0,0)

and each turn consists of passing an edge and moving to adjacent vertex. In how many ways can the robot go back to

(0,0,0,0)

after

4042

turns? Note that it is NOT forbidden for the robot to pass through

(0,0,0,0)

before the

4042

-nd turn.

Problem Statement