XK-MO 2014

A student read the book with $480$ pages two times. If he in the second time for every day read $16$ pages more than in the first time and he finished it $5$ days earlier than in the first time. For how many days did he read the book in the first time?

The number $2015$ has been written in the table. Two friends play this game: In the table they write the difference of the number in the table and one of its factors. The game is lost by the one who reaches $0$ . Which of the two can secure victory?

A square $ABCD$ with sude length 1 is given and a circle with diameter $AD$ . Find the radius of the circumcircle of this figure.