9.8

Part of IV Soros Olympiad 1997 - 98 (Russia)

Problems(2)

king in 6x6 chessboard (IV Soros Olympiad 1997-98 Correspondence 9.8)

Source:

There is a king in the lower left corner of a chessboard of dimensions

6

6

. In one move, he can move either one cell to the right, or one cell up, or one cell diagonally - to the right and up. How many different paths can the king take to the upper right corner of the board?

combinatoricscombinatorial geometry

P(P(P(x))) = 0 if P(x) = x^2+bx+c (IV Soros Olympiad 1997-98 R3 9.8)

Source:

P(x) = 0

P(x) = x^2+bx+c

, has a single root, and the equation

P(P(P(x))) = 0

has exactly three different roots. Solve the equation

P(P(P(x))) = 0.

algebrapolynomial