We need to have at least one computer game in our collection, of course. The typical one could be described as "chase in the town". The smiling face called Jack in our case is walking through the town divided into small fields. Some of the fields are covered with the wall and it is not possible to go through them. Jack collects the points and tries to avoid contact with the monsters who chase him. Once the Jack eats the special point (or asterisk), the situation turns upside-down and Jack can eat monsters. And so on, still again and again. I am sure everyone of you have ever seen such game.
The town is randomly generated in our case. Jack always starts in the top left corner and the "bonus asterisk" is in the bottom right corner. At the most difficult level, the bonus is set to disappear after exactly as much steps that are sufficient to get from one corner to another, providing Jack only makes steps to the left and to the bottom. Should he made one single step into the wrong direction and he never could be there in time. But it is still important to prevent being catched by monsters. So the player has to choose the best possible way to the bottom right corner. You are to determine how many different ways exist in the town.