Date: Jun 14, 1996 4:03 AM
Author: Joel Neely
Subject: Re: "Impossible Problem"

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.

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.