Re: MathsBombe - observations but not the answer

In article <vobinl$1jvp$1@macpro.inf.ed.ac.uk>,
Richard Tobin <richard@cogsci.ed.ac.uk> wrote:

In article <vo9t64$hlp5$2@dont-email.me>,
David Entwistle  <qnivq.ragjvfgyr@ogvagrearg.pbz> wrote:

Please don't post a direct answer to the question posed, but I'd welcome a
bit of guidance on Mathsbombe question 3.

I have guessed the correct answer without understanding the problem.

I have now understood the problem (and its solution).

Let me clarify the points that have caused some doubt about the
problem itself.

(1) The coins have value x^0 (=1), x^1 (=x), x^2, x^3, ... for some
    irrational x > 3.3.

(2) Any positive integer amount can be made.  This will require an
    unlimited number of coins in total, but not more than 14 of any
    single value.

Here are some obvious observations:

(1) We could equally well consider the problem to be representing an
    integer in the irrational base x, where the digits are 0 .. 14.

(2) We need to find an irrational x such that we can add multiples of
    its powers to get integers.  That rules out x being transcendental
    by definition.

And finally a hint that should not give much away until you are on the
right track:

You may, like me, stumble upon the correct value of x and then see
that it works for numbers up to N - a number greater than 400 - but
not immediately see how it works beyond that.  I had to think of it
somewhat differently to see that it does.

-- Richard