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The problem you uploaded involves dividing 12 items among three players (A, B, and C) using the method of markers. Each player places markers at certain intervals, and based on these markers, the items are divided. Here’s how to interpret the diagram and answer the questions:

1. **Items and Players' Markers:**
   - Items are numbered 1 through 12.
   - The players have placed their markers at the following positions:
     - Player A: \(A_1\) is between items 4 and 5, and \(A_2\) is between items 7 and 8.
     - Player B: \(B_1\) is between items 8 and 9, and \(B_2\) is between items 9 and 10.
     - Player C: \(C_1\) is between items 3 and 4, and \(C_2\) is between items 6 and 7.

### Answering the Questions:

1. **Which player receives item 1?**
   - Player C's first marker \(C_1\) is after item 3, meaning Player C claims items up to item 3.
   - So, **Player C** receives item 1.

2. **Which player receives item 5?**
   - Player A's first marker \(A_1\) is after item 4, so Player A claims items 4 and 5.
   - **Player A** receives item 5.

3. **Which player receives item 11?**
   - Player B's second marker \(B_2\) is after item 10, so Player B claims item 11.
   - **Player B** receives item 11.

4. **Which items are left over?**
   - After distributing the items based on the players' markers:
     - Player C gets items 1, 2, and 3.
     - Player A gets items 4, 5, 6, and 7.
     - Player B gets items 8, 9, 10, 11, and 12.
   - No items are left over. Hence, **none** of the items are left over.

### Would you like to know more details or have any questions?

### Related Questions:
1. What is the method of markers in asset division?
2. Why did Player A receive items 4 through 7?
3. How would the result change if Player C placed their first marker after item 2?
4. Can this method be applied if there were four players instead of three?
5. What is the significance of each player's second marker?

### Tip:
The method of markers is a fair division method used to divide discrete items when players have different preferences over the items, ensuring each player gets a "fair share."

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

Explore how players A, B, and C use the method of Markers to divide 12 items fairly. This problem is a practical application of fair division methods, focusing on identifying which player receives specific items based on their markers. Suitable for students in Grades 10-12.

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