SHOW STEPS BY STEP OF THIS:
Play
• For players of your maze game, the goal is to move from the starting point to
the ending point using the shortest possible path—the path that requires
traveling the least total distance.
• Players can only move through the maze in horizontal or vertical directions.
They cannot move diagonally or through polygons.
• Show and code two trial games. Use colored pencils or markers to draw two
different paths through the maze. Use coordinates to describe each path.
• The device will use the coordinates for each path to mathematically calculate
the total distance. Show how the device will calculate the total distance for
each trial path that you drew.
• Is either trial path the shortest possible path? Explain.
Step 1: Draw the maze
- Begin by creating a maze with a starting point, ending point, and multiple paths between them. Be sure to include several polygons (barriers) to make the paths more challenging.
Step 2: Create two trial games
- Use colored pencils or markers to draw two different paths through the maze. Each path should move only in horizontal or vertical directions, and not pass through any polygons.
Step 3: Record the coordinates
- Make a note of the coordinates for each turn in both trial paths. This will help in visualizing the paths and calculating the distances.
Example:
Trial 1 Path: (0,0) -> (1,0) -> (1,1) -> (2,1) -> (2,2) -> (3,2)
Trial 2 Path: (0,0) -> (0,1) -> (1,1) -> (1,2) -> (2,2) -> (3,2)
Step 4: Calculate the total distance for each path
- The device will use the coordinates to calculate the total distance for each trial path. It can be done by counting the number of units moved horizontally and vertically along each path.
Example:
Trial 1 Distance: 1 (right) + 1 (up) + 1 (right) + 1 (up) + 1 (right) = 5 units
Trial 2 Distance: 1 (up) + 1 (right) + 1 (up) + 1 (right) + 1 (right) = 5 units
Step 5: Determine the shortest possible path
- Compare the total distance of each trial path and determine if any of them is the shortest possible path. If they are equal in distance, then both might be the shortest, but if there's a difference, the one with the shorter distance is the better path.
Example:
In the example provided, both trials have a total distance of 5 units. Without evaluating other possible routes through the maze, it is difficult to say if these are the shortest possible paths. To confirm the shortest path, all possible routes through the maze should be evaluated and their distances calculated, then compared to find the shortest one.