Apollo 11

In 1969 'the Eagle has landed' on the Moon and a few days later the upper section of the lunar module brought Armstrong and Aldrin back to the command and service module, which finally brought the astronauts back to Earth.
But what happened to the lunar module? Does it still circle the Moon five decades later?
If you find this question interesting you may like this YouTube video.
I think it is a great example of what dedicated space and science enthusiasts can do ...


Consider the equation xxx.. = 2.
How do you find x in this iterated exponentiation, a.k.a hyperpower?
The solution is quite easy: Consider the 'tower' above the bottom x, ie. xx...
But it is the same as the original 'tower', so we know it is 2.
Therefore x2 = 2 and it follows that x = sqrt(2).

But there is a problem if we now consider the equation xxx.. = 4.
Using the same argument we find x4 = 4, with the same solution x = sqrt(2).
Clearly there is a contradiction; it seems that we just proved that 2 = 4 if we equate the 'towers' of sqrt(2).

I found this math exercise and the solution to the puzzle here.

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