Henry Ernest Dudeney/Puzzles and Curious Problems/100 - Digital Squares

by : $100$

 * Digital Squares
 * Find a number which, together with its square, shall contain all the $9$ digits once, and once only, the $0$ disallowed.
 * Thus, if the square of $378$ happened to be $152 \, 694$, it would be a perfect solution.
 * But unfortunately the actual square is $142 \, 884$, which gives us repeated $4$s and $8$s, and omits the $6$, $5$, and $9$.


 * There are only two possible cases, and these may be discovered in about a quarter of an hour if you proceed in the right way.