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Re: "Impossible Problem"
Posted:
Jun 14, 1996 4:03 AM


Brian Raiter wrote: > A similar problem ... > Fill in the blanks so as to make this whole page logically > selfconsistent. > > 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 10tuples to 10tuples. I.e., fill in the blanks with the values of the argument 10tuple, then count the digits to get the resultant 10tuple.
Now iterate.
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.



