Which of these years has an identical calendar layout to 2011?

The correct option is 2022.

To find which year has a calendar layout completely identical to the year 2011, two fundamental rules of the calendar must be fulfilled:
1. Both years must be of the same category (either both must be ordinary non-leap years, or both must be leap years).
2. The net number of odd days accumulated between the two years must be 0 (or a multiple of 7), ensuring that both years begin on the exact same day of the week.

Step 1: Identify the type of year for 2011
The year 2011 is not divisible by 4, making it an ordinary year of 365 days.

Step 2: Calculate the odd days between 2011 and 2022
An ordinary year (365 days = 52 weeks + 1 day) gives 1 odd day.
A leap year (366 days = 52 weeks + 2 days) gives 2 odd days.

The number of years between 2011 and 2022 is calculated as:

$2022-2011=11\text{years}$

Within this 11-year interval, we count the leap years: 2012, 2016, and 2020. This gives us:
• Number of leap years = 3
• Number of ordinary years = 11 - 3 = 8

Next, we compute the total number of odd days accumulated:

$\text{Total odd days}=(8\times 1)+(3\times 2)$

$\text{Total odd days}=8+6=14$

To find the net odd days, we take the total modulo 7:

$14\text{mod}7=0$

Step 3: Verification and Conclusion
Because the net count of odd days is 0, both 2011 and 2022 start on the exact same day of the week (Saturday). Additionally, since 2022 is also an ordinary non-leap year, its calendar layout is completely identical to that of 2011.