Mathematics is about far more than numbers and shapes - it is fundamentally about patterns, and such patterns come in many forms. Imagine looking at a game of chess as it evolves from move to move. Every move changes the pattern on the chess board. At the end of the game the rules of chess determine whether the final pattern is a victory for white, for black or ends in a draw.
The mathematics of game theory aims to analyse games so as to find winning strategies. It has a wide range of applications in fields such as economics, biology and psychology. Now, chess is a game with simple rules yet complex strategies; far too hard for us to start with! So let's look at something simpler.
One of the favourite games at my after-school club is Mouse Trap. It is a simple game where a computer-operated mouse tries to escape from a hexagonal grid while you try to encircle it by blocking its path with bricks. You win if you manage to trap the mouse so it can no longer move; you lose if the mouse manages to reach the edge of the grid and thus escape.
Go to Mouse Trap now!
Play the game a few times and get a feel for how to trap the mouse.
This question is to write out a winning strategy. Be as precise as possible so that someone could write a computer program that takes your rules and applies them to every specific situation. This does not have to be a long essay! You should be able to describe your winning strategy in just four or five sentences.
One additional question: does your strategy win all the time?
Have fun!
Tuesday, 15 May 2012
2 comments:
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There are some rules you must follow to win the game.
ReplyDelete1. Control the mouse's path by putting blocks the opposite direction you want the mouse to follow.
2. Drive mouse to pre-existing blocks.
3. DO NOT let the mouse get to one square away from the perimeter.
4. Trap the mouse inside big shape made from pillars, then enclose in a hexagon of sides 1.
Hi Catherine
Deleteinteresting set of rules, however, 1 and 2 talk about the mouse, but you don't know where it will go.
You move first, so how do you decide where to place that first block?
Then, depending on the mouse move, how do you decide where to place the next, say, 4 or 5 blocks?