Zschess & Ivanight
Source: Junior Olympiad of Malaysia 2014 P2
July 20, 2015
combinatorics
Problem Statement
In ZS Chess, an Ivanight attacks like a knight, except that if the attacked square is out of range, it goes
through the edge and comes out from the other side of the board, and attacks that square instead. The
ZS chessboard is an 8 \times 8 board, where cells are coloured with distinct colours, where is a natural
number, such that a Ivanight placed on any square attacks squares that consist of all colours, and
the colours appear equally many times in those squares. For which values of does such a ZS chess
board exist?