https://file.aiquickdraw.com/mathbot/file/172660599419082paja4j.jpg

The problem you're dealing with uses the "method of markers" to divide assets (numbered items from 1 to 12) among three players, A, B, and C. Each player has placed their markers to indicate their preference for groups of items. 

### Key Details from the Image:
- Players A, B, and C have markers at the following positions:
  - **Player A**: Markers at 1 and 8 (A₁ and A₂).
  - **Player B**: Markers at 7 and 10 (B₁ and B₂).
  - **Player C**: Markers at 3 and 9 (C₁ and C₂).

#### Dividing the Assets:
1. From **marker A₁ to marker C₁** (items 1 to 3):
   - Player **C** receives items 1 to 3.

2. From **marker C₁ to marker B₁** (items 4 to 7):
   - Player **B** receives items 4 to 7.

3. From **marker B₁ to marker A₂** (items 8 and 9):
   - Player **A** receives items 8 and 9.

4. From **marker A₂ to marker B₂** (items 10 to 10):
   - Player **B** receives item 10.

5. From **marker B₂ onwards** (items 11 and 12):
   - Player **A** receives items 11 and 12.

#### Answering the Questions:
1. **Which player receives item 1?**
   - Player **C**.

2. **Which player receives item 5?**
   - Player **B**.

3. **Which player receives item 11?**
   - Player **A**.

4. **Which items are left over?**
   - No items are left over, so this question seems to involve a trick. However, based on your selections, the correct choice would be **None of the items** (since all are allocated). But among the given options, none fits perfectly. If forced to choose, "8, 9, 10, 11, and 12" seems closest based on how the problem is framed, though all assets are actually distributed.

Would you like more clarification or details on how the method of markers works? Let me know if you want to explore this more.

Here are some related questions:
1. What would happen if a player placed their markers at different positions?
2. How does the method of markers ensure fairness?
3. Could the assets be divided equally among more than three players?
4. What strategy should a player use to maximize their outcome in the method of markers?
5. How would the solution change if there were 15 items instead of 12?

**Tip:** The method of markers works best when each player carefully places their markers to balance between gaining their most valued items and ensuring they get as many items as possible.

Players A, B, and C have placed their markers to divide up twelve assets using the method of markers. Which player receives item 1? Which player receives item 5? Which player receives item 11? Which items are left over?

Solve the method of markers problem to divide 12 assets between players A, B, and C. Learn how each player's items are determined and which items are left over, if any.

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