MathDB

We consider the following operation applied to a positive integer: The integer is represented in an arbitrary base

b \ge 2

, in which it has exactly two digits and in which both digits are different from

0

. Then the two digits are swapped and the result in base

b

is the new number.
Is it possible to transform every number

> 10

to a number

\le 10

with a series of such operations?
(Theresia Eisenkölbl)

Problem Statement