What is the next following number for 512 12?

Answer 1

According to Wittgenstein's Finite Rule Paradox every finite sequence of numbers can be a described in infinitely many ways and so can be continued any of these ways - some simple, some complicated but all equally valid. Here, for example, the answer could be

• 2 : delete on digit from the left
  
• -488 : Arithmetic progression, with Un = 1012 - 5*n
• 0.28125 : Geometric progression with U1 = 512 and U(n+1) = Un*(3/128)
• 4.78 (approx) : U(n+1) = 4*3*log(Un) where the logarithm is to base 2.

I could think of hundreds more which, in the right context, would make absolutely good sense.