MathDB
Numbering fields of chessboard

Source:

September 8, 2010
modular arithmeticcombinatoricsChessboardIMO Shortlist

Problem Statement

(a) Decide whether the fields of the 8×88 \times 8 chessboard can be numbered by the numbers 1,2,,641, 2, \dots , 64 in such a way that the sum of the four numbers in each of its parts of one of the forms
http://www.artofproblemsolving.com/Forum/download/file.php?id=28446
is divisible by four.
(b) Solve the analogous problem for
http://www.artofproblemsolving.com/Forum/download/file.php?id=28447