Henry Ernest Dudeney/Puzzles and Curious Problems/155 - The Orchard Problem

Puzzles and Curious Problems by Henry Ernest Dudeney: $155$

The Orchard Problem

A market gardener was planting a new orchard.

The young trees were arranged in rows so as to form a square,

and it was found that there were $146$ trees unplanted.

To enlarge the square by an extra row each way he had to buy $31$ additional trees.

How many trees were there in the orchard when it was finished?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $155$. -- The Orchard Problem
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $228$. The Orchard Problem