My friend whose a newer cuber said He saw a video on youtube where they said there were enough combinations on the petaminx to fill up 15 universes. How many things are wrong with that?
There are more?
Let's just look at the teraminx which I found a firm number on the # of combinations for (petaminx obviously has more but I haven't seen a good looking calculation)
1.7989 x 10^571 possible positions. Drewseph says his teraminx fits in an 11x11x11cm cube. A dodecahedron's edge length is approximately half its cubic dimensions so I'll go with 5.5cm per edge. A dodecahedron's volume is IIRC approximately equal to 7.66*(edge length^3) so the volume of a teraminx is approximately 1274.4325 cubic centimeters. Going with 13.7 billion light years for the radius of the universe, light traveling at 3*10^8m/s, we get 4/3*pi*((1.37*10^10)*(3600*24*365)*(3*10^8)*(100))^3 cubic centimeters in the universe.
1274.4325*1.7989*10^571
= 2.29257662*10^574 cm^3 for all possible teraminx positions, assuming we can seamlessly pack teraminxes together.
4/3*pi*((1.37*10^10)*(3600*24*365)*(3*10^8)*(100))^3
= 1.4043993*10^85 cm^3 in the universe
Obviously the petaminx would fill even more universes.