Problem 1
 ABC is acute angle triangle with AB<>AC. The circle with diameter BC
 intersects the lines AB and AC respectively at M and N. O is the
 midpoint of BC. The bisectors of <BAC and <MON intersect at R.
 Prove that the circumcircles of thev triangles BMR and CNR have a
 common point lying on the line BC.
 
 Problem 2
 Find all polynomials f with real coefficients such that, for all
 reals a,b,c such that ab+bc+ca = 0, we have the relation
 f(a-b) + f(b-c) + f(c-a) = 2 f(a+b+c)
 
 Problem 3
 Define a "hook" to be a figure made up of six unit squares as shown
 in the figure below, or any of the figures obtained by rotations and
 reflections to this figure.
 [ ][ ][ ]
 [ ]   [ ]
 [ ]
 Determine all mxn rectangles that can be covered without gaps and
 without overlaps with hooks such that no point of a hook covers area
 outside the rectangle
 
 Problem 4
 Let n>=3 be an integer. Let t[1],...,t[n] be positive real numbers
 such that
 n^2+1>(t[1]+...+t[n])(1/t[1]+...+1/t[n])
 Show that, for all distinct i,j,k, t[i],t[j],t[k] are the side
 lengths of a triangle
 
 Problem 5
 In a convex quadrilateral ABCD, the diagonal BD bisects neither <ABC
 nor <CDA. A point P lies inside ABCD and satisfies <PBC = <DBA
 and <PDC = <BDA.
 Prove that ABCD are concyclic if and only if AP = CP.
 
 Problem 6
 A positive integer is alternating if every two consecutive digits in
 its decimal representation are of different parity. Find all
 positive integers n such that n has a multiple which is alternating.