Henry Ernest Dudeney/Puzzles and Curious Problems/92 - Digits and Squares/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $92$

Digits and Squares

$(1) \quad$ What is the smallest square number, and

$(2) \quad$ what is the largest square number

that contains all the ten digits ($1$ to $9$ and $0$) once, and once only?

Solution

From Smallest Pandigital Square:

$1 \, 026 \, 753 \, 849 = 32 \, 043^2$

From Largest Pandigital Square:

$9 \, 814 \, 072 \, 356 = 99 \, 066^2$

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $92$. -- Digits and Squares
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $129$. Digits and Squares