MathDB

An antelope is a chess piece which moves similarly to the knight: two cells

(x_1,y_1)

and

(x_2,y_2)

are joined by an antelope move if and only if

\{|x_1-x_2|,|y_1-y_2|\}=\{3,4\}.

The numbers from

1

10^{12}

are placed in the cells of a

10^6\times 10^6

grid. Let

D

be the set of all absolute differences of the form

|a-b|

, where

a

and

b

are joined by an antelope move in the arrangement. How many arrangements are there such that

D

contains exactly four elements?
Proposed by Nikolai Beluhov, Bulgaria

Problem Statement