sounds like a perfect idea for a multiplayer server.
could be my next project, hahahaha

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let's upgrade this game to hexagonal board!
man! distance metric on a hexagonal board is the best.

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> Одна из стратегий игры — забраться в резиновую комнату и управлять медведем, наводя его на других игроков.

sounds like a whole new game.
imagine all users can do this simultaneously.
a bear that copies each move of all players, so that calculating a superposition of moves.
assuming a clean board with N players and 1 bear, and complete information, does this game have a trivial strategy?

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