Brian Raiter wrote: > A similar problem ... > Fill in the blanks so as to make this whole page logically > self-consistent. > > On this page, the digit zero appears times. [snip] > " nine " times. ... > Clifford Pickover describes this problem, and mentions that Martin > Gardner has shown that there is only one solution.
And an interesting approach (described, I think, in a Sci Am article by MG) is to treat the set of sentences as a function mapping from 10-tuples to 10-tuples. I.e., fill in the blanks with the values of the argument 10-tuple, then count the digits to get the resultant 10-tuple.
Depending on the initial value, the iteration will either cycle through a set of tuples (length > 1) or converge to a solution tuple (i.e., a cycle of length 1).
Someone with better discrete dynamical systems skills than I have might address the question of which properties of an initial value could be used to predict which kind of basic that initial tuple lies in.