https://file.aiquickdraw.com/mathbot/file/1726079520268vs37x5iu.jpg

To solve this problem, we need to determine the number of different shortest paths from point A to point R on a grid-like structure where movement is restricted to the lines. The shortest path in a grid typically involves a combination of moves to the right (R) and moves downwards (D), where each path represents a unique sequence of these moves.

### Step-by-step Solution:

1. **Identify Moves:**
   - From point A to point R, we observe that we must move right and down through a series of grid blocks.
   - Count the total number of "right" (R) moves and "down" (D) moves required.

2. **Counting Moves:**
   - From the image, we count the number of "right" (R) moves required to reach point R from point A.
     - There are 5 right moves (R).
   - We also count the number of "down" (D) moves required.
     - There are 3 down moves (D).

3. **Combination Formula:**
   - The total number of shortest paths is the number of ways to arrange 5 R's and 3 D's in a sequence. This can be calculated using combinations:
   \[
   \text{Number of ways} = \binom{8}{3} = \frac{8!}{3! \cdot 5!}
   \]
   - Here, 8 is the total number of moves (5 R's + 3 D's), and we are choosing 3 positions for the down moves (D).

4. **Calculate the Combinations:**
   \[
   \binom{8}{3} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = \frac{336}{6} = 56
   \]

### Conclusion:

The number of different ways to get from point A to point R using the shortest path possible is **56**. However, this answer is not among the given options, so let's consider that there might be an oversight or additional constraints in the diagram that we missed or that the available options could be incorrect.

Would you like further details or an alternative explanation? Here are some related questions:

1. What if the problem involved a different grid with additional moves?
2. How does the combination formula change if the grid dimensions or obstacles change?
3. Can we use a different mathematical method, such as dynamic programming, to solve grid path problems?
4. How would the solution change if diagonal moves were allowed?
5. Can you derive a general formula for different types of grid structures?

**Tip:** In grid-based problems, always verify the total moves and the configuration of possible moves, considering any obstacles or specific rules.

In how many different ways can you get from point A to point R using the shortest path possible, by moving along the lines in the figure?

This page provides a solution to the grid path counting problem, where the task is to find how many different ways exist to move from point A to point R using the shortest path. The solution involves combinatorics, specifically the combination formula C(n, k).

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