TITLE: Apocorubik's Cube (10,000 blocks across): How long to solve if a quarter turn takes 2.8 seconds?
QUESTION [8 upvotes]: Suppose you have a Rubik's cube, $10,000$ blocks across (so, $600,000,000$
total tiles), scrambled.  Assuming an ideal solving algorithm, approximately how long will the cube take to be solved, given one quarter turn can be made every 2.8 seconds?

REPLY [4 votes]: According to https://arxiv.org/abs/1106.5736 the asymptotic bound for God's Number on higher order cubes is:
$$\Theta(n^2/\log n)$$
But this is only asymptotic, so you can't just plug in $n$ and expect to get the exact right answer.  But we use it as a very loose approximation.  Since God's Number for $n=3$ is 26 (using quarter-turn metric), we can do:
$$
\frac{10000^2}{\log 10000} * \frac{\log 3}{3^2} * 26 = 34458757
$$
So to round off your question take that number, multiply it by 2.8s, and you get about 3.1 years.