Henry Ernest Dudeney/Modern Puzzles/61 - Palindromic Square Numbers/Solution
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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?
Solution
Dudeney gives:
- $836^2 = 698896$
This is now known to be the smallest.
There are larger ones, but they are fairly rare.
Also see
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $61$. -- Palindromic Square Numbers
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $112$. Palindromic Square Numbers