5
$\begingroup$

Is it possible for the number created by the consecutive numbers $1$ to $n$ where $n > 1$ be a palindrome eg. $1234567\ldots n$?

I believe this is a contest problem, but how would one solve this problem without looking up the hints?

  • 3
    @Day,$1$19 8 17 6 15 4 13 2 10 20 12 3 14 5 16 7 18 9 11.2011-08-17

1 Answers 1

2

A solution can be found on page 43 of Andreescu and Andrica, Number Theory: Structures, Examples, and Problems, which page I was able to access on Google Books.

  • 1
    For those who do not want to read it thoroughly, if $10^5$ is the largest degree of $10$ before $n$, then there is only one piece $...99991000010001...$ with $0000$, which thus should be in the center of palindrome, but is not symmetric.2018-03-15