MathDB

Let

\mathbb Z_{\ge 0}

be the set of non-negative integers, and let

f:\mathbb Z_{\ge 0}\times \mathbb Z_{\ge 0} \to \mathbb Z_{\ge 0}

be a bijection such that whenever

f(x_1,y_1) > f(x_2, y_2)

, we have

f(x_1+1, y_1) > f(x_2 + 1, y_2)

and

f(x_1, y_1+1) > f(x_2, y_2+1)

.
Let

N

be the number of pairs of integers

(x,y)

with

0\le x,y<100

, such that

f(x,y)

is odd. Find the smallest and largest possible values of

N

Problem Statement