Peer-Reviewed Journal Details
Mandatory Fields
Escamocher, Guillaume; O’Sullivan, Barry
Discrete Mathematics
Leprechauns on the chessboard
Optional Fields
Assignment diversity Constraint satisfaction n-Queens Problem
We introduce in this paper leprechauns, fairy chess pieces that can move either like the standard queen, or to any tile within k king moves. We then study the problem of placing n leprechauns on an n×n chessboard. When k=1, this is equivalent to the standard n-Queens Problem. We solve the problem for k=2, as well as for k>2 and n=(k+1)2, giving in the process an upper bound on the lowest non-trivial value of n such that the (k,n)-Leprechauns Problem is satisfiable. Solving this problem for all k would be equivalent to solving the diverse n-Queens Problem, the variant of the n-Queens Problem where the distance between the two closest queens is maximized. While diversity has been a popular topic in other constraint problems, this is not the case for the n-Queens Problem, making our results the first major ones in the domain.
Grant Details
Science Foundation Ireland
Grant No.12/RC/2289-P2