Next: Project 4: Work the Up: W4444 Programming and Problem Previous: Project 2: Planet Builder
In 2003, I gave a project involving cutting cookies from a piece of dough. This year we're doing something different: competitive cookie cutting! This is a game for two players, played on a 50x50 grid of dough. Each player designs three cookie cutter shapes (details below) and tries to cut out as much of the dough as possible before the dough runs out. The score is the total area of dough that your player manages to capture. Your primary goal is to capture more dough than your opponent (as opposed to maximizing the amount of dough), so defensive strategies that block your opponent while blocking yourself to a lesser degree are worth considering.
You get to make three cutters of size 11, 8, and 5 units. These cutters must be a connected orthogonal set of unit squares. So the 5-unit shape must be one of the 12 possible pentominos, for example. (Actually, since we don't consider reflective symmetries, there are more than 12 choices: how many are there?) Each player creates their 11-unit shape first and submits it to the simulator. The simulator shares this information with both players, who then select their 8-unit shape. After the simulator informs both players of the 8-unit selection, players submit their 5-unit shapes. So players get to design the smaller shapes in light of the known choices of both players for the larger shapes.
One final rule about selecting shapes. The simulator will not allow players to select the same shape (taking the four rotational symmetries into account). If players happen to select the same shape, both players' choices are rejected and players have to select a new shape, different from all previous choices. If the simulator has to reject players' shapes 5 times in a row, then the simulator will randomly assign one of the five choices to each player (a different shape to each).
The game is played by placing a cookie-cutter of your choice anywhere on the board in one of the four orthogonal orientations. You may only select a location if there is dough remaining within each cell delimited by the cookie cutter. Note that the cookie-cutter cannot include partial dough cells: the perimeter defined by the cookie-cutter must lie on the ``grid lines'' of the dough grid. At the end of the turn, your score is incremented by the size of the cutter used, and the corresponding dough is removed from the grid. Players take turns, but to balance the game the first player must use the 5-unit cutter on the first turn.
Some things to think about:
Ken Ross 2015-09-21