# Puzzles

## Princess problem

A princess lives in a row of 17 rooms. Each day she moves to a room adjacent to the one she wakes up in (eg. If she sleeps in room 5 today, then she will sleep in room 4 or 6 tomorrow). If you are able to find the princess by only opening one door each night then you will become her prince. Can you find her in a finite number of moves?

#### Show answer & extension

#### Hide answer & extension

Imagine a chessboard with 17 columns and a large number of rows. Let each column correspond to one of the rooms. In the first row, mark the room in which the princess is. Every day following, mark her location in the next row.

The princess will always move one square diagonally, so will always be on the same colour square she started on. Begin by checking the 17th room, then the 16th room, then continue down the the first room. If the princess started on a black square you will have found her, as she has no way of getting past you.

If you have not caught the princess, then she must have started on a white square. Checking rooms 17 down to one again will find her as this time it will start on a white square.

#### Extension

Is there a quicker way to find the princess?