You are playing a video game, your character is in a town of dragons and is running low on his life meter. there are 4 door in this town and each door is guarded by 10 dragons. you know that behind three of the four doors are bottomless pits and if you open one of them you will get sucked in and your character will die. the other door though has a magic sword behind it that will restore your life to full and will you to defeat the saber-toothed bunny in the next level of the game. the dragons will answer your yes and no questions, but each dragon only knows what is behind his own door. also, of the 40 dragons, three of them lie. further, though the dragons are friendly, they have terrible breath and each time one speaks a word to you your life meter goes down. devise a non-adaptive, way to determine which door the sword is behind that involves you asking as few yes/no questions as possible. be sure to justify why your solution is optimal.