Question 64
Show that there exist two distinct positive integers $a, b$, each having exactly 2014 digits (in base ten; initial zeroes disallowed), with the following properties.
* The digits of $b$ are those of $a$ in reverse order.
* When a digit in each of $a$ and $b$ is deleted at random, and the resulting numbers are denoted $a'$ and $b'$, respectively, then
$$
\frac{a'}{b'} = \frac{a}{b}
$$
with a likelihood exceeding 99%.
* The digits of $b$ are those of $a$ in reverse order.
* When a digit in each of $a$ and $b$ is deleted at random, and the resulting numbers are denoted $a'$ and $b'$, respectively, then
$$
\frac{a'}{b'} = \frac{a}{b}
$$
with a likelihood exceeding 99%.