Spot it(R) Solitaire

TL;DR

This paper explores the mathematical structure of the game Spot it(R), focusing on arranging its cards to reveal the symmetries of an order 7 affine plane, and addresses the inverse problem of card arrangement.

Contribution

It introduces a novel challenge of arranging Spot it(R) cards to illustrate affine and projective plane symmetries, emphasizing the inverse problem of deck arrangement.

Findings

Successful arrangement of 49 cards into a symmetric square

Demonstration of affine and projective plane symmetries

Method for solving the inverse arrangement problem

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.