In the year 2016 there are 52 complete weeks and some extra days. If the total number of days in 2016 is 366, how many extra days P does the year contain beyond the 52 full weeks?

Introduction / Context:
This question focuses on the simple relationship between total days in a year and the number of complete weeks plus extra days. The year 2016 is a leap year, so it has 366 days. We are asked to express 2016 in the form of 52 weeks and P days, and find the value of P. This type of calculation is frequently used in calendar questions involving odd days and day of week computations.

Given Data / Assumptions:

• The year 2016 has 366 days.
• One week has 7 days.
• The year is expressed as 52 weeks plus P days.
• We need to find the integer P, the number of extra days.

Concept / Approach:
The approach is straightforward. We divide the total number of days in the year by 7 to find how many complete weeks fit into that total, and then we look at the remainder. The quotient corresponds to the number of full weeks and the remainder corresponds to the number of extra days beyond those weeks. Since the question already states 52 weeks, we focus on finding the remainder when 366 is divided by 7.

Step-by-Step Solution:
Step 1: Total days in 2016 are 366, because it is a leap year. Step 2: Divide 366 by 7 to find the number of complete weeks and the remainder. Step 3: Compute 7 * 52 = 364 days. Step 4: Subtract 364 from 366. The remainder is 366 − 364 = 2 days. Step 5: Therefore, 366 days can be written as 52 weeks and 2 days. Step 6: The value of P representing the extra days is 2.

Verification / Alternative check:
You can verify by rewriting the expression: 52 weeks equal 52 * 7 = 364 days, and adding 2 more days gives 364 + 2 = 366 days, which matches the total days of a leap year. The fact that 2016 is a leap year is consistent with this because most ordinary years have 365 = 52 weeks and 1 day, while leap years have one additional extra day, resulting in 52 weeks and 2 days. This matches the well known pattern that leap years shift the starting weekday of the next year by two days instead of one.

Why Other Options Are Wrong:
If P were 3, we would have 52 weeks and 3 days, which would total 364 + 3 = 367 days, which is not correct for 2016. Similarly, P equal to 4 or 5 would give 368 or 369 days, clearly impossible for any standard year. An answer of 4 or 5 would conflict with even the simple fact that no standard Gregorian year contains more than 366 days. Therefore, only P equal to 2 is consistent with 366 days in total.

Common Pitfalls:
Students sometimes confuse the number of extra days in leap years and ordinary years, or they might incorrectly multiply or divide when working with weeks. Another common mistake is to treat the expression 52 weeks and P days as approximate instead of exact, leading to acceptance of incorrect values for P. To avoid errors, always perform the explicit division of days by 7 and interpret the quotient and remainder directly as full weeks and leftover days.

Final Answer:
So, in 2016 there are 52 weeks and 2 extra days, meaning P = 2.