1

Part of 2007 International Zhautykov Olympiad

Problems(2)

easy n x n table problem

Source: Third Zhautykov Olympiad, Kazakhstan, 2007

There are given

111

n\times n

table divided into unit cells. This coins are placed inside the unit cells (one unit cell may contain one coin, many coins, or may be empty), such that the difference between the number of coins from two neighbouring cells (that have a common edge) is

1

. Find the maximal

n

for this to be possible.

combinatorics proposedcombinatorics

functional ecuation, a bit strange, but not difficult

Source: Third Zhautykov Olympiad, Kazakhstan, 2007

Does there exist a function

f: \mathbb{R}\rightarrow\mathbb{R}

f(x+f(y))=f(x)+\sin y

, for all reals

x,y

functiontrigonometrygeometrygeometric transformationalgebra proposedalgebra