Ooh, that's really neat. I want to also explore the asymmetry of executioner and civilian. What is the real meaning of ending someone's life? Why does one life matter over another? Why does one person get to take that life? And each time you play, there's a different criminal condemned to the eternal punishment of death. It would also be neat to explore the afterlife, even having the executioner meet all the people they killed. (That would mean that maybe it can't be completed during recess, but who knows)
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Though not listed on the main page, I think a major part of hangman is that every time you play a different game. Almost every time, the word or phrase that you are guessing will be different. There are many ways that one could represent this in a game, video or otherwise. I plan to have the game's story vary each time, and hopefully it doesn't seem forced like many random games do. It would also be neat to see a game from the point of view of the executioner or the hanged, rather than a third party.
after creating a game, you typically submit binaries (compiled code) to run on different systems (typically windows, mac, and some variant/variants of linux, to make it accessible for most)
if it is not a video game, it is up to you how to submit. In the future, give more information in you question.