Determine the Day of the Week for the 27th Day of a Month Given the 10th is Saturday

Understanding how to determine the day of the week for any given date is a valuable skill in both mathematics and practical life. In this article, we'll explore the process of figuring out the day of the week for the 27th of a month when we know that the 10th falls on a Saturday. This mathematical exercise involves a series of steps that are both logical and straightforward.

Understanding the Problem

We are given a specific condition: if the 10th day of a month is a Saturday, we need to determine the day of the week for the 27th day of the same month. This problem requires us to calculate the number of days between these two dates and then use that information to figure out the number of days before the next Saturday.

Step-by-Step Solution

Let's break down the process step by step:

Step 1: Calculate the Number of Days Between the 10th and 27th

From the 10th to the 27th of a month, we have:

27 - 10 17 days

So, we have 17 days between the 10th and the 27th of the month.

Step 2: Simplify Using Modular Arithmetic

To make the calculation easier, we can use modular arithmetic to simplify the days. We know that:

17 ≡ 3 (mod 7)

This means that 17 days is equivalent to 3 days in a week. Since a week has 7 days, any multiple of 7 days can be ignored in our calculation.

Step 3: Determine the Day of the Week

Given that the 10th day is a Saturday, we need to find out three days after Saturday.

The days of the week are: Saturday, Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and then back to Saturday, and so on.

So, if the 10th is a Saturday, then:

10th Saturday

11th Sunday

12th Monday

13th Tuesday

Therefore, the 27th day falls on a Tuesday.

Conclusion

Whenever the 10th day of a month is a Saturday, the 27th day of the same month will fall on a Tuesday. This is a clear and straightforward result. The key takeaway from this problem is the use of modular arithmetic in solving date-related problems.

Keywords

day calculation, calendar math, Saturday to Tuesday

References

1. Math is Fun

2. Cut the Knot

3. Math Problems