Room squares with holes of sides 3,5, and 7

Abstract

We investigate Room squares with small holes: missing subsquares of sides 3, 5 or 7. We refer to a Room square of side s missing a subsquare of side t as an ( s, t)-incomplete Room square. For any odd t, it has been shown that there is an integer S( t) such that an ( s, t)-incomplete Room square exists for all odd s> S( t). In this paper we prove that S(3)⩽39, S(5)⩽67, and S(7)⩽53.