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

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*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?*

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## 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