Henry Ernest Dudeney/Modern Puzzles/61 - Palindromic Square Numbers

by : $61$

 * Palindromic Square Numbers
 * This is a curious subject for investigation -- the search for square numbers the figures of which read backwards and forwards alike.
 * Some of them are very easily found.
 * For example, the squares of $1$, $11$, $111$ and $1111$ are respectively $1$, $121$, $12321$, and $1234321$, all palindromes,
 * and the rule applies for any number of $1$'s provided the number does not contain more than nine.


 * But there are other cases that we may call irregular, such as the square of $264 = 69696$ and the square of $2285 = 5221225$.
 * Now, all the examples I have given contain an odd number of digits.


 * Can the reader find a case where the square palindrome contains an even number of figures?

Also see

 * Square of Small-Digit Palindromic Number is Palindromic
 * Palindromic Squares with Non-Palindromic Roots