Minimum Number of Newspapers Required to Satisfy All Students

The question often posed in logical and mathematical puzzles is: 'A school has 300 students. 1 student reads 5 newspapers and 1 newspaper is read by 60 students. What is the minimum number of newspapers required?' This problem challenges us to think critically about the distribution and usage of newspapers to satisfy all students' reading preferences. Let's break down the solution step-by-step to understand how to find the answer.

Understanding the Problem

The problem can be understood through a clear understanding of the given conditions. We know that 1 student reads 5 newspapers and 1 newspaper is read by 60 students.

Interpreting the Conditions

1. If 1 student reads 5 newspapers, it means there are 5 separate reads for each of the 5 newspapers. Therefore, for a single student, there are 5 newspapers being accessed.

2. If 1 newspaper is read by 60 students, it means one newspaper is being shared among 60 different students. This implies that each of these 60 students is contributing one read to this single newspaper.

Calculating Total Reads

Given that there are 300 students, we can calculate the total number of reads required. Since each student reads 5 newspapers, the total number of reads can be calculated as:

[ text{Total reads} 300 times 5 1500 ]

This means there are 1500 read attempts across all newspapers.

Relationship Between Total Reads and Newspapers

If one newspaper is read by 60 students, then each newspaper will go through 60 different read sessions. We need to determine how many such newspapers are required to satisfy 1500 read attempts.

The relationship can be expressed as:

[ text{Total reads} 60 times x ]

Where ( x ) is the number of required newspapers. To find ( x ), we set up the equation:

[ 1500 60 times x ]

Solving for ( x ):

[ x frac{1500}{60} 25 ]

Therefore, the minimum number of newspapers required is 25.

Intuitive Approach

An intuitive approach to solving the problem can be achieved by breaking it down into smaller batches of students. If each student reads 5 newspapers, we can distribute the newspapers in such a way that each newspaper is read by 60 students. Here’s a breakdown:

The first 60 students read 5 different newspapers (N1, N2, N3, N4, N5). The next batch of 60 students (from student 61 to 120) read the next 5 different newspapers (N6, N7, N8, N9, N10), and so on. This pattern continues until all 300 students have read their respective 5 newspapers.

Following this pattern, we can see that each of the 25 newspapers will be read by 60 students. As such, the minimum number of newspapers required is 25.

This matches the mathematical solution derived in the previous sections, and it ensures that all 300 students have the opportunity to read their preferred 5 newspapers.

Key Takeaways:

The total number of read attempts is 1500. Each newspaper is read by 60 students. To satisfy 1500 read attempts, 25 newspapers are required.

Understanding the problem's core through breakdown and calculation can help in solving similar logical and combinatorial puzzles.

Thanks for exploring this interesting question! If you have any more puzzles or questions, feel free to ask!