Spot it(R) Solitaire

Abstract: The game of Spot it(R) is based on an order 7 finite projective plane. This article presents a solitaire challenge: extract an order 7 affine plane and arrange those 49 cards into a square such that the symmetries of the affine and projective planes are obvious. The objective is not to simply create such a deck already in this solved position. Rather, it is to solve the inverse problem of arranging the cards of such a deck which has already been created shuffled.