How to Share Apples Equally Among Friends: A Practical Solution

Paige, a thoughtful and generous friend, is faced with the challenge of sharing 11 identical apples among 30 of her friends. The goal is to distribute the apples equally without slicing any apple into more than 10 pieces. This article provides a detailed plan on how to achieve this objective efficiently and fairly.

Introduction to the Problem

At the heart of the problem is the need to ensure that all 30 friends receive an equal share of the apples, while adhering to the constraint of not exceeding 10 pieces per apple. Paige desires to maintain the integrity of the apples as much as possible, but ultimately, the wellbeing and satisfaction of her friends are the top priority.

Understanding the Constraint

The constraint that no apple can be sliced into more than 10 pieces is a significant one. It means that Paige must think creatively and carefully about how to approach the distribution. Each apple can therefore yield a maximum of 10 individual pieces, which contributes to the complexity of the task.

Step-by-Step Solution

Step 1: Divide Five Apples into Six Pieces

To start, Paige should select five of the 11 available apples. By cutting each of these five apples into six pieces, she can create a total of 30 pieces. This method ensures that every friend can receive one piece from these five apples. Here's how to do it:

Select five apples. Cut each of these five apples into six parts. Distribute one sixteenth of an apple to each of the 30 friends.

Step 2: Distribute the Remaining Apples into Five Parts

After distributing the first set of 30 pieces, Paige will have six apples left. These six apples need to be divided into five groups of six pieces each. Here's the step-by-step process:

Select the remaining six apples. Cut each apple into five pieces. Distribute these additional five pieces to each friend.

Final Check and Distribution

Once all the apples have been cut and distributed, it's important for Paige to double-check the distribution to ensure that every friend has received five pieces. The method described ensures that the distribution is both fair and adheres to the constraint of not exceeding 10 pieces per apple.

Benefits of the Solution

Equity: Every friend receives an equal share of the 11 apples, which is a critical aspect of any group sharing activity. Integrity: The apples are only cut into a small number of pieces, preserving their natural form and ensuring that no apple is overly damaged. Efficiency: The process is straightforward and requires minimal preparation and time. It ensures that the distribution is both fast and efficient.

Conclusion

Sharing 11 identical apples among 30 friends requires creative thinking and careful planning. By following the steps outlined in this article, Paige can ensure that the distribution is fair, efficient, and adheres to the constraint of not exceeding 10 pieces per apple. This method not only satisfies everyone involved but also demonstrates a thoughtful and practical approach to sharing resources.