# Understand the problem

plays 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 such

that player Pi has beaten Pi+1 for all i = 1, 2, . . . , n.

##### Source of the problem

I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance Examination 2016. Subjective Problem no.1.

##### Topic

##### Difficulty Level

7 out of 10

##### Suggested Book

# Start with hints

we define a sequence \(p_1\)>\(p_2\)>\(p_3\)………..>\(p_n\) . such that \(p_i>p_{i+1}\) implies \(p_i\) has beaten \(p_{i+1}\)

let assume that the statement is true for n=k i.e \(p_1> p_2>p_3………p_k\) now look into the case of \(p_{k+1}\)

if \(p_{k+1}\) > \(p_1\) or \(p_k\)>\(p_{k+1}\) we are done (why?)

# Connected Program at Cheenta

# I.S.I. & C.M.I. Entrance Program

Indian Statistical Institute and Chennai Mathematical Institute offer challenging bachelor’s program for gifted students. These courses are B.Stat and B.Math program in I.S.I., B.Sc. Math in C.M.I.

The entrances to these programs are far more challenging than usual engineering entrances. Cheenta offers an intense, problem-driven program for these two entrances.