MathDB

30\times30

table is given. We want to color some of it's unit squares such that any colored square has at most

k

neighbors. ( Two squares

(i,j)

and

(x,y)

are called neighbors if

i-x,j-y\equiv0,-1,1 \pmod {30}

and

(i,j)\neq(x,y)

. Therefore, each square has exactly

8

neighbors) What is the maximum possible number of colored squares if

:

a) k=6

b)k=1

Problem Statement