A square army plus one straggler reforms into 113 equal smaller squares
A band of Crusaders could be drawn up as one giant square formation. Add a single extra man, and the whole company could instead be arranged as 113 separate smaller squares, all exactly the same size, with nobody left over. How many men were there in total?
Reveal the answer
602,177 men. The original force of 602,176 men formed one square (776 x 776). Adding one man gives 602,177, which splits evenly into 113 squares of 5,329 men each (73 x 73), since 113 x 73-squared equals 602,177. From Henry Dudeney's The Canterbury Puzzles (1907).
— Henry Dudeney, The Canterbury Puzzles — 1907, 'The Riddle of the Crusaders'