While making some algebraic problems last summer for an examination, I devised the following question:—

“A schoolmaster went mad, and amused himself by arranging the boys. He turned the dux boy down one place, the new dux two places, the next three, and so on till every boy's place had been altered at least once. Then he began again, and so on; till, after 306 turnings down, all the boys got back to their original places. This disgusted him, and he kicked one boy out. Then he was amazed to find that he had to operate 1120 times before all got back to their original places. How many boys were in the class?”