1 Solve the following system for real triplets
2 Let be the vertices of an sided regular polygon in that order. Determine , given that
3 Let be a quadrilateral inscribed in a circle. Suppose and subtends an angle of at the centre of the circle. Find the maximum possible area of the quadrilateral .
4 Let be positive real numbers such that . Prove that
5 Find all real numbers such that , where denotes the greatest integer less than or equal to .
6 In a book of page numbers from to , some pages are torn off. The sum of the numbers on the remaining pages is . How many pages are torn off?
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