We introduce an impartial combinatorial game on Steiner triple systems calledNofil . Players move alternately, choosing points of the triple system . If a player is forced to fill a block on their turn, they lose . The game Nofil can be thought of in terms of play on a corresponding hypergraph . As game play progresses, the hypergraph shrinks and will eventually be equivalent to playing the game Node Kayles on anisomorphic graph . We conclude that the complexity of determining the outcome of the game on Nofil isPSPACE-complete. We explore the playof Nofil on all Steiner . systems up to order 15 and a sampling for orders19, 21, and 25 . We determine the optimal strategies by computing the nim-values

Author(s) : Melissa A. Huggan, Svenja Huntemann, Brett Stevens

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Keywords : game - nofil - steiner - triple - systems -

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