Understand the problem Let be a real-valued function on the plane such that for every square in the plane, Does it follow that for all points in the plane? Source of the problem Putnam 2009 A1 Topic Geometry Difficulty Level Easy Suggested Book Mathematical...

Understand the problem In a badminton singles tournament, each player played against all the othersexactly once and each game had a winner. After all the games, each playerlisted the names of all the players she defeated as well as the names of all theplayers defeated...

Understand the problem Given a triangle ABC with three lattice vertices . it is known that no more lattice point lies on the edges . only one lattice point D is inside the triangle . prove that D is centroid of that triangle . Source of the problem Iran Maths...

Understand the problem Let (a,b,c) be the sides of a triangle and (A,B,C) be the angles opposite to those sides respectively. If ( sin (A-B)=frac{a}{a+b}sin Acos B-frac{b}{a+b} cos A sin B), then prove that the triangle is isosceles. Source of the problem I.S.I....

Understand the problem Suppose that in a sports tournament featuring n players, each pairplays one game and there is always a winner and a loser (no draws).Show that the players can be arranged in an order P1, P2, . . . , Pn suchthat player Pi has beaten Pi+1 for all...

Understand the problem Let be a polynomial with integer coefficients. Define and for .If there exists a natural number such that , then prove that either or . Source of the problem I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance Examination...