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

Puzzles and Curious Problems by Henry Ernest Dudeney: $100$

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.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $100$. -- Digital Squares
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $130$. Digital Squares