Variations on the theme of the Greenberger-Horne-Zeilinger proof

Three arguments based on the Greenberger-Horne-Zeilinger (GHZ) proof of the nonexistence of local hidden variables are presented. The first is a descr iption of a simple game which a team that uses the GHZ method will always w in. The second uses counterfactuals in an attempt to show that quantum theo ry is nonlocal in a stronger sense than is implied by the nonexistence of l ocal hidden variables and the third describes peculiar features of time-sym metrized counterfactuals in quantum theory.