If today is Friday, which day will it be after 72 days?
Sunday
Understanding Day Calculations Over Time
This question asks us to determine the day of the week after a specific number of days, starting from a given day. The key to solving such problems is understanding the cyclic nature of days of the week.
The 7-Day Cycle
There are 7 days in a week: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday. This sequence repeats every 7 days. This means that after 7 days, 14 days, 21 days, or any multiple of 7 days, the day of the week will be the same as the starting day.
Calculating the Day After 72 Days
To find the day after 72 days, we need to figure out how many full weeks pass and what the remaining number of days is. The remainder after dividing the total number of days by 7 tells us how many days forward from the starting day we need to count.
Step-by-Step Calculation:
- Identify the total number of days given: 72 days.
- Identify the starting day: Friday.
- Divide the total number of days (72) by the number of days in a week (7) to find the remainder.
Let's perform the division:
\( 72 \div 7 \)
We can write 72 as:
\( 72 = (7 \times 10) + 2 \)
Here, 10 is the quotient (number of full weeks) and 2 is the remainder.
Interpreting the Remainder
The remainder is 2. This means that after 10 full weeks (70 days), the day will be the same as the starting day (Friday). We then need to count 2 additional days from Friday.
- Day 1 after Friday is Saturday.
- Day 2 after Friday is Sunday.
Therefore, after 72 days, it will be Sunday.
Summary of the Calculation
| Starting Day | Number of Days | Calculation | Remainder | Days to Count Forward | Resulting Day |
|---|---|---|---|---|---|
| Friday | 72 | \(72 \div 7\) | 2 | 2 (from Friday) | Sunday |
The calculation confirms that 72 days after Friday is Sunday.
Revision Table: Day Calculation Concepts
| Concept | Explanation | Application |
|---|---|---|
| 7-Day Cycle | Days repeat every 7 days (Mon, Tue, ..., Sun). | Basis for calculating future days. |
| Modulo Arithmetic | Finding the remainder after division. | Used to find the position within the cycle. |
| Remainder 0 | Number of days is a multiple of 7. | Resulting day is the same as the starting day. |
| Remainder n (1-6) | Number of days is n more than a multiple of 7. | Resulting day is 'n' days after the starting day. |
Additional Information on Cyclic Time Problems
Problems involving repeating cycles, like days of the week, months, or even hours on a clock, can often be solved using the concept of modulo arithmetic (finding the remainder). The general approach is:
- Identify the length of the cycle (e.g., 7 for days, 12 for months on a clock, 24 for hours).
- Determine the total number of steps (days, months, hours, etc.).
- Divide the total number of steps by the cycle length.
- The remainder tells you how many steps into the cycle the end point is, relative to the starting point.
For example, if a clock shows 9 o'clock and you want to know what time it will be after 50 hours, you'd divide 50 by 24 (cycle length for hours). \(50 \div 24 = 2\) with a remainder of 2. Starting from 9, you count 2 hours forward (9 + 2 = 11). It would be 11 o'clock.
This method is versatile and applicable to various problems involving repeating sequences.
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