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

Modern Puzzles by Henry Ernest Dudeney: $61$

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

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $61$. -- Palindromic Square Numbers
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $112$. Palindromic Square Numbers