Henry Ernest Dudeney/Puzzles and Curious Problems/85 - Squares and Triangulars/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $85$

Squares and Triangulars

What is the third lowest number that is both a triangular and a square?

$1$ and $36$ are the two lowest which fulfil the conditions.

What is the next number?

Solution

$1225$

Proof

See Triangular Numbers which are also Square.

$\blacksquare$

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $85$. -- Squares and Triangulars
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $187$. Squares and Triangulars