Henry Ernest Dudeney/Modern Puzzles/53 - Squares and Digits/Solution
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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.
Solution
- $1444 = 38^2$
Proof
See Squares Ending in Repeated Digits.
$\blacksquare$
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $53$. -- Squares and Digits
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $104$. Squares and Digits