MathDB

Six members of the team of Fatalia for the International Mathematical Olympiad are selected from

13

candidates. At the TST the candidates got

a_1,a_2, \ldots, a_{13}

points with

a_i \neq a_j

i \neq j

.
The team leader has already

6

candidates and now wants to see them and nobody other in the team. With that end in view he constructs a polynomial

P(x)

and finds the creative potential of each candidate by the formula

c_i = P(a_i)

.
For what minimum

n

can he always find a polynomial

P(x)

of degree not exceeding

n

such that the creative potential of all

6

candidates is strictly more than that of the

7

others?
Proposed by F. Petrov, K. Sukhov

2