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On the existence of Spot It! decks that are not projective planes Cover

On the existence of Spot It! decks that are not projective planes

Open Access
|Mar 2024

Abstract

The game Spot It! is played with a deck of cards in which every pair of cards has exactly one matching symbol and the aim is to be the fastest at finding the match. It is known that finite projective planes correspond to decks in which every card contains n symbols and every symbol appears on n cards. In this paper we relax the hypothesis on the number of cards on which a symbol appears: we study symmetric decks in which every symbol appears the same number of times and we introduce the concept of maximal deck, providing a sufficient condition for a deck to have this property. We also produce various examples of interesting decks which do not correspond to projective planes.

Language: English
Page range: 31 - 50
Published on: Mar 8, 2024
Published by: Ludus Association
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2024 Bianca Gouthier, Daniele Gouthier, published by Ludus Association
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.