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We are given a figure in which all the central dots are collinear, and the bottom three dots are also collinear. There are exactly 2024 triangles that can be formed using the dots as vertices, where no three collinear dots form a triangle. We are tasked with determining how many dots there are in total.

### Step-by-step solution:

1. **Total Number of Dots**:
   Let's denote the total number of dots as \( n \). If there are \( n \) dots, the total number of ways to choose 3 dots (to potentially form a triangle) is given by the combination formula:
   \[
   \binom{n}{3} = \frac{n(n-1)(n-2)}{6}
   \]
   However, since no three collinear dots form a triangle, this directly gives us the number of triangles.

2. **Number of Triangles**:
   We are told that exactly 2024 triangles can be formed. Therefore, we set up the equation:
   \[
   \binom{n}{3} = 2024
   \]
   This simplifies to:
   \[
   \frac{n(n-1)(n-2)}{6} = 2024
   \]
   Multiply both sides by 6:
   \[
   n(n-1)(n-2) = 12144
   \]

3. **Solve for \( n \)**:
   Now, we solve this equation for \( n \). Testing values of \( n \):

   - For \( n = 16 \):
   \[
   16 \times 15 \times 14 = 3360
   \]
   - For \( n = 12 \):
   \[
   12 \times 11 \times 10 = 1320
   \]
   Let me test further and find the accurate value.

   I'll compute that now.The equation \( n(n-1)(n-2) = 12144 \) gives a real solution of \( n = 24 \). The other two solutions are complex and therefore not valid for this context.

Thus, the total number of dots is \( \boxed{24} \).

Would you like any further details, or have any questions?

Here are some related questions you might find useful:

1. How many ways can we select 3 points from 24 to form triangles?
2. How would the number of triangles change if we added more dots?
3. Can this method be generalized to different shapes, not just triangles?
4. What if some dots were collinear, affecting the count of possible triangles?
5. How would the number of triangles change if the number of dots were halved?

**Tip**: Remember that when dealing with combinations like this, the formula \( \binom{n}{k} \) provides the number of ways to choose \( k \) elements from \( n \) without regard to order!

In the following figure, all the central dots are collinear, and the bottom three dots are collinear. There are exactly 2024 triangles that have dots as vertices (no three collinear dots form a triangle). How many dots are there?

Learn how to solve a combinatorics problem where you are tasked with finding the number of dots in a geometric configuration that can form exactly 2024 triangles. This problem requires using the combination formula to determine the total number of dots.

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