throwing an octahedron 10 times, 1 side painted red and 7 painted blue
Source: Dutch NMO 1997 p4
January 29, 2020
octahedronColoringcombinatoricscombinatorial geometry
Problem Statement
We look at an octahedron, a regular octahedron, having painted one of the side surfaces red and the other seven surfaces blue. We throw the octahedron like a die. The surface that comes up is painted: if it is red it is painted blue and if it is blue it is painted red. Then we throw the octahedron again and paint it again according to the above rule. In total we throw the octahedron times. How many different octahedra can we get after finishing the th time?Two octahedra are different if they cannot be converted into each other by rotation.