Problem 3

The country of Totalia has money with special values: they issue a 1 pound coin as well as coins with irrational values of $x^k$ pounds for $k=0,1,2, \ldots$, where $x$ is a certain fixed number greater than $3.3$. While highly unusual, this system has a certain benefit: any positive integer cost can be paid by using no more than 14 coins of every given denomination. What number $x$ do Totalians use? Give your answer rounded to 4 decimal points.

To deter guessing without thinking, we ask that you also solve the following simple arithmetic problem before checking your answer:

What is 3 + 9 - 7?

This problem was first solved on Thu 6th February at 3:21:23pm