Problems 50–60 do not match the examples in this text, but all the problem-solving techniques necessary to answer these questions have been covered in this text. These problems are designed to test your problem-solving abilities.

An army general of the cavalry would always deploy his army in formation, and that formation was in the form of a square. However, when he did this, he saw that he had 284 soldiers left over that would not fit into the square formation. So, he decided to regroup the soldiers into another square formation by increasing each side by one soldier, but this time he was short 25 soldiers. How many soldiers are in this general’s army? This question was formulated from a problem by the famous mathematician Colin Maclaurin (1698–1746).