Henry Ernest Dudeney/Modern Puzzles/53 - Squares and Digits

Modern Puzzles by Henry Ernest Dudeney: $53$

Squares and Digits

What is the smallest square number that terminates with the greatest possible number of similar digits?

Thus the greatest possible number might be $5$ and the smallest square number with $5$ similar digits at the end might be $24677777$.

But this is certainly not a square number.

Of course, $0$ is not to be regarded as a digit.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $53$. -- Squares and Digits
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $104$. Squares and Digits