8
Part of 1995 All-Russian Olympiad
Problems(2)
board 2000×2000 with 1 and -1
Source: All-Russian olympiad 1995, Grade 9, Second Day, Problem 8
10/21/2013
Numbers 1 and −1 are written in the cells of a board 2000×2000. It is known that the sum of all the numbers in the board is positive. Show that one can select 1000 rows and 1000 columns such that the sum of numbers written in their intersection cells is at least 1000.
D. Karpov
combinatoricsgraph theory
sum of the squares of the coeficients of the P(x)Q(x)
Source: All-Russian olympiad 1995, Grade 10, Second Day, Problem 8
10/20/2013
Let and be monic polynomials. Prove that the sum of the squares of the coeficients of the polynomial is not smaller than the sum of the squares of the free coefficients of and .
A. Galochkin, O. Ljashko
algebrapolynomial