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The problem states:

- There are 100 pages divided into four groups of 25 pages each: \(1-25\), \(26-50\), \(51-75\), and \(76-100\).
- Each group must be assigned to one of four printers, with each printer capable of printing either \(0\), \(25\), \(50\), \(75\), or \(100\) pages in total.
- We need to find the number of ways to assign these groups of pages to the four printers.

### Solution

This is a combinatorial problem where each group of 25 pages can be independently assigned to one of four printers, and each printer can take a combination of 0, 25, 50, 75, or 100 pages. To determine the total number of assignments, consider that:

1. **Each group of 25 pages** can be assigned to any of the four printers, giving us 4 choices per group.
2. **There are four groups**, so the total number of assignments is \(4 \times 4 \times 4 \times 4 = 4^4\).

### Calculating the Total Number of Assignments
\[
4^4 = 256
\]

### Conclusion
There are **256 possible ways** to assign the 100 pages to the four printers based on the given conditions.

Would you like further details or have any questions?

Here are some related questions for further exploration:

1. What if each printer had a different maximum capacity?
2. How would the answer change if each printer could only handle exactly one of the 25-page groups?
3. What if the groups were not of equal size?
4. How many ways would there be if each group could only go to a unique printer?
5. What if there were constraints on how many pages each printer could handle in total?

**Tip:** When solving combinatorial problems, start by identifying independent choices and calculate the total by multiplying the number of choices for each independent selection.

Suppose that all the pages are black-and-white, but each group of 25 consecutive pages (1–25, 26–50, 51–75, 76–100) must be assigned to the same printer. Each printer can be assigned 0, 25, 50, 75, or 100 pages to print. How many ways are there for the 100 pages to be assigned to the four printers?

Explore a combinatorial solution to assigning 100 pages, divided into groups of 25, to four printers. Each group must be assigned to one of four printers, with each printer capable of handling 0, 25, 50, 75, or 100 pages. This problem highlights independent choices and the multiplication principle in combinatorics, suitable for Grades 10-12.

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