GIVEN: Starting from point A of the cube shown below, a beetle can travel around the bottom
perimeter in exactly four minutes. NOTE: the beetle can climb up or across the cube's sides.
REQ'D: Answer the following Questions:
1. What is the minimum amount of time it would take the beetle to get from point A to point B,
assuming it travels at the same rate of speed as it did around the perimeter?
2. How many different solutions are there?
Remember to document your solution procedure by presenting your results in standard engineering
problem set format

To solve this problem, we need to consider the shortest path for the beetle to travel from point A to point B while following the perimeter of the cube. Since the beetle can climb up or across the cube's sides, it can traverse the edges of the cube.

Given:

- Time taken to travel around the bottom perimeter of the cube: 4 minutes

1. To find the minimum time for the beetle to travel from point A to point B:

- The shortest path from point A to point B follows the bottom perimeter for 3 edges and then climbs up the vertical edge to reach point B.

- Since each edge takes 4 minutes to traverse, and there are 3 edges to traverse horizontally, the time taken for horizontal traversal is 3 * 4 = 12 minutes.

- Additionally, the beetle needs to climb up one vertical edge, which also takes 4 minutes.

- Therefore, the minimum amount of time for the beetle to travel from point A to point B is 12 minutes (horizontal traversal) + 4 minutes (vertical traversal) = 16 minutes.

2. To determine the number of different solutions:

- There is only one shortest path for the beetle to travel from point A to point B, as described above.

- Therefore, there is only one solution.

In summary:

1. Minimum time for the beetle to travel from point A to point B: 16 minutes

2. Number of different solutions: 1