8

Part of 2020 Caucasus Mathematical Olympiad

Problems(2)

Inequality with condition abc+a+b+c=ab+bc+ca+5

Source: 2020 Caucasus Mathematical Olympiad

a

b

c

abc+a+b+c=ab+bc+ca+5.

Find the least possible value of

a^2+b^2+c^2

inequalitiesalgebraHigh school olympiad

Find the greatest n satisfying given condition

Source: 2020 Caucasus Mathematical Olympiad Seniors Problem 8

100

distinct integers on a board. Basil needs to fill the cells of a table

100\times{100}

with integers so that the sum in each rectangle

1\times{3}

(either vertical, or horizontal) is equal to one of the numbers written on the board. Find the greatest

n

such that, regardless of numbers written by Peter, Basil can fill the table so that it would contain each of numbers

(1,2,...,n)

at least once (and possibly some other integers).

combinatoricsCombinatorial games