MathDB

Joe makes two cubes of sidelengths

9

and

10

from

1729

randomly oriented and randomly arranged unit cubes, which are initially unpainted. These cubes are dipped into white paint. Then two cubes of sidelengths

1

and

12

are formed from the same unit cubes, again randomly oriented and randomly arranged, and these cubes are dipped into paint remover. Joe continues to alternately dip cubes of sides

9

and

10

into paint and cubes of sides

1

and

12

into paint remover ad nauseam. What is the limit of the expected number of painted unit cube faces immediately after dipping in paint remover?

Problem Statement