1. **Problem statement:** There are 4 housekeepers working on each floor. Each room requires one housekeeper. If the housekeepers try to distribute the work equally, how many housekeepers need to clean more rooms than the others? 2. **Understanding the problem:** We want to divide the total number of rooms on a floor among 4 housekeepers as evenly as possible. Some housekeepers may have to clean one more room if the total number of rooms is not divisible by 4. 3. **Formula and rules:** - Let $R$ be the total number of rooms on the floor. - Let $H = 4$ be the number of housekeepers. - When dividing $R$ by $H$, the quotient $q = \lfloor \frac{R}{H} \rfloor$ is the number of rooms each housekeeper cleans if evenly distributed. - The remainder $r = R \bmod H$ is the number of housekeepers who must clean one extra room. 4. **Key point:** The number of housekeepers who clean more rooms than others is exactly the remainder $r$. 5. **Example:** - If $R = 10$ rooms and $H = 4$ housekeepers, - Then $q = \lfloor \frac{10}{4} \rfloor = 2$ rooms each, - And $r = 10 \bmod 4 = 2$ housekeepers clean 3 rooms instead of 2. 6. **Conclusion:** To find how many housekeepers clean more rooms, find the remainder when the total rooms are divided by 4. Since the problem does not specify the total number of rooms $R$, the answer is: **Number of housekeepers cleaning more rooms = $R \bmod 4$**. If you provide the total number of rooms, I can calculate the exact number.