Henry Ernest Dudeney/Puzzles and Curious Problems/174 - More Curious Multiplication/Solution 2

by : $174$

 * More Curious Multiplication

Solution
As points out: all numbers such as:
 * $1001$
 * $10101$
 * $100101$

that is, numbers made up of $1$ and $0$, with $1$ at each end and no two consecutive instances of $1$.

notes that you can't rule out numbers of the form $[1 0 d_1 d_2 \ldots d_n 0 1]_{10}$, although at the left hand end you may need to make sure your carry digit does not affect the second digit.