Select Page ## A function on squares

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... ## Extremal Principle : I.S.I Entrance 2013 problem 4

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... ## Lattice point inside a triangle

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... ## An isosceles triangle,on Trigonometry, I.S.I Entrance 2016, Solution to Subjective problem no. 6

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....

## I.S.I 2016 SUBJECTIVE PROBLEM – 1

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...

## ISI 2019 : Problem #7

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...