Arithmetic Sequence

In the year-end ceremony, 12 top-performing CMM students form a line. Each of them holds a different number from 1 to 12. Dr. Hong calls their numbers one at a time to give them awards. At first, Dr. Hong tries to call the numbers so that no three of them form an arithmetic sequence. What's the maximum number of students Dr. Hong calls before he sees an arithmetic sequence of at least three numbers.

Circle in a Right Triangle

A circle is inscribed in a right triangle of leg lengths 8 and 15. What's the area of this circle? (Let Pi = 3.14.)

Squares and Median

The sum of 3 different positive integers is 55. The sum of any two of them is a perfect square. What is the median of these three positive integers?