IMO 2022 Shortlist C9
Let Zě0 be the set of non-negative integers, and let f : Zě0 ˆ Zě0 Ñ Zě0 be a bijection such that whenever fpx1,y1q ą fp...
Category: Combinatorics
Problem
Let Zě0 be the set of non-negative integers, and let f : Zě0 ˆ Zě0 Ñ Zě0 be a
bijection such that whenever fpx1,y1q ą fpx2,y2q, we have fpx1 1,y1q ą fpx2 1,y2q and
fpx1,y1 1q ą fpx2,y2 1q.
Let N be the number of pairs of integers px,yq, with 0 ď x,y ă 100, such that fpx,yq is
odd. Find the smallest and largest possible value of N.
(U.S.A.) 6 Oslo, Norway, 6th–16th July 2022