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

by : $53$

 * 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.