Calendar – Same-year pattern: Which is the next year after 1991 that shares the same calendar as 1990?

Introduction / Context:Two years share the same calendar if all month layouts match (weekday of Jan 1 and leap/common status align so that all dates fall on the same weekdays). We want the next year after 1991 that matches the 1990 calendar.

Given Data / Assumptions:

• Reference year: 1990 (a common year).
• Find the next year after 1991 with an identical calendar to 1990.

Concept / Approach:For a common (non-leap) year, the same calendar generally repeats after 6 or 11 years depending on how leap years shift weekday starts. We test candidates after 1991, checking both leap status and weekday alignment.

Step-by-Step Solution:1) 1990 is a common year starting Monday; its exact month-by-month pattern is fixed.2) Check subsequent common years until all months align. The next match is 2001.3) Therefore 2001 is the first year after 1991 that shares 1990’s calendar.

Verification / Alternative check:Compare month calendars for 1990 and 2001; each month layout (date vs weekday) matches. Many almanacs or calendar algorithms confirm this.

Why Other Options Are Wrong:1998, 2002, 2003 → their Jan 1 weekdays/leap offsets do not produce identical month layouts to 1990.

Common Pitfalls:Assuming a constant 6-year repeat for all common years without checking intervening leap years.

Final Answer:2001