4 papers
Generalizing OOOOOOB
Alon Danai, Paul Ellis, Thotsaporn Aek Thanatipanonda
We present three versions of the classic two-pile game \textsc{one-or-one-or-one-of-both} generalized to the multi-pile context. In each case, we explore the resulting $\mathcal{P}…
Two Dimensional Subtraction -- Transfer Games
Alon Danai, Paul Ellis, Thotsaporn Aek Thanatipanonda
We generalize the results and conjectures of Tamás Lengyel, showing that the \textsc{nim}-values of a large class of two-dimensional subtraction-transfer games are periodic. These…
The Penults of Tak: Adventures in impartial, normal-play, positional games
Boris Alexeev, Paul Ellis, Michael Richter +1
For normal play, impartial games, we define penults as those positions in which every option results in an immediate win for the other player. We explore the number of tokens in pe…
Two Games on Arithmetic Functions: SALIQUANT and NONTOTIENT
Paul Ellis, Jason Shi, Thotsaporn Aek Thanatipanonda +1
We investigate the Sprague-Grundy sequences for two normal-play impartial games based on arithmetic functions, first described by Iannucci and Larsson in \cite{sum}. In each game,…