MathDB

For all integers

x,y

, a non-negative integer

f(x,y)

is written on the point

(x,y)

on the coordinate plane. Initially,

f(0,0) = 4

and the value written on all remaining points is

0

. For integers

n, m

that satisfies

f(n,m) \ge 2

, define '[color=#9a00ff]Seehang' as the act of reducing

f(n,m)

1

, selecting 3 of

f(n,m+1), f(n,m-1), f(n+1,m), f(n-1,m)

and increasing them by 1. Prove that after a finite number of '[color=#0f0][color=#9a00ff]Seehang's, it cannot be

f(n,m)\le 1

for all integers

n,m

Problem Statement