Mathematical Brain Teaser #4

Can you help a prince and a princess find each other? If you know math, this should be easy.

A princess inhabits a flight of 17 rooms in a row. Each room has a door to the outside, and there is a door between adjacent rooms. The princess spends each day in a room that is adjacent to the room she was in the day before. One day a prince arrives from far away to woo for the princess. The guardian explains the habits of the princess and also the rules to him: Each day he may knock at an outside door of his choice. If the princess is behind it she will open and in the end marry him. If not, nothing happens, and he gets another chance the next day. Unfortunately his return ticket expires after 30 days. Does he have enough time to conquer the princess?

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2 Comments.

  1. Very nice riddle!

    30 days should be enough. Number the doors (or rooms) 1 to 17 and assume that the princess is in an even room.

    On the first day knock on door 2. If she is not there, she must be in another even room, which means that the next day she will move to an odd(-numbered) room. This can be any odd room, but not room 1, since she is currently not in room 2.

    To continue, on the second day knock on door 3. The next day knock on door 4, etc. Note that she cannot get past you, because we know whether she is in an even or odd room (if our initial assumption was correct), therefore she is never in a room adjacent to the one we are checking.

    Keep going, until on day 15, you knock on door 16. The princess must be in this room, since she couldn’t have passed you and she is in an even room. What? She’s not answering? Well then, either she is deaf, or it would seem that our initial assumption was incorrect. No worries, we still have 15 days left. Let’s see…

    We now _know_ that on day 1 she was in an odd room. So on day 16, she will be in an even room! So let’s start again then.

    On day 16 knock on door number 2. The next day, knock on door number 3…

    Finally, after 30 days, we get to knock on door number 16 again, but this time we _know_ that she is there.
    “Tag, you’re it!”

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  2. I think it depends on which room she started with. When the prince got there she may have been in room 5 or 4 who knows.. which room she was in the first place.. if its a habbit she may have started a long time ago.

    If the princess knew that the prince was looking for her. She could have started from room number 1. but then it would have made it easier for him to find her.

    As for whether the prince can find her within 30 days… there’s plenty of time… I think….

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