Rapunzel and the Prince

The evil witch has left Rapunzel and the prince in the center of a completely dark, large, square prison room. The room is guarded by four silent monsters in each of its corners.  Rapunzel and the prince need to reach the only escape door located in the center of one of the walls, without getting near the foul beasts. How can they do this, considering they can not see anything and do not know in which direction to go?

The prince must stay in the center of the room and hold Rapunzel’s hair, gradually releasing it. Then, Rapunzel must walk in circles around the prince, until she gets to the walls and finds the escape door.

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  1. Could another answer be the next?

    They put their feet together, facing the same direction, and one of them turns around 45º. They can do that with an easy play of feet. The prince holds Rapunzel’s hair and both start walking forward slowly until one of them touches a wall. Then, the other one stops and follows the hair.

    Assuming that we divide that big square room into 4 smaller squares, and these 4 squares, in turn, into 2 right triangles, we know that the hypotenuse of the triangles are longer than the legs.

    When one of them turns 45º, they are forming a hypothetical right triangle, knowing that one of them will walk through one leg while the other walks through the hypotenuse. Of course, when one of them touches a wall, they must alert the other one to stop walking, because he/she could be facing one of the beasts. This strategy would work in any direction, always walking 45º away one from each other.

    For instance, if Rapunzel walks directly to the beast in the top-right corner, the prince would touch the wall before she meets it. Therefore, the prince would tell Rapunzel to stop and to follow his hair’s trace. Even if that’s not the wall of the door, Rapunzel could still walk 90º, to the opposite direction, while counting the number of steps she takes. If she realizes that that wall is neither the one of the door, she could retreat a half of the number of steps she walked, getting again to the center of the room, rotate 90º and try again. If, again, the wall she touches is not the correct one, she’ll know for sure that the opposite will be, through process of elimination.

    It’s a way more complex than the original solution XD. If I’m making any mistake, please, correct me again ^u^

    1. That’s a great solution. It is a bit harder to perform, since Rapunzel and the Prince need to walk straight and with similar speeds, but I like the geometry of it. Well done Kera! 🙂