Solution
The Calendar Returns
Show the problem again
A year's calendar is the same as another year's if every date falls on the same weekday, which requires the two years to have equal length and to begin on the same weekday. Use the Gregorian calendar. 2026 is not a leap year and begins on a Thursday. What is the first year after 2026 whose calendar is identical to 2026's? Give the year.
Worked solution
A common year shifts the starting weekday forward by 1 and a leap year by 2. From 2026, moving to 2027, 2028, ... the shifts are 1, 1, 2 (2028 leap), 1, 1, 1, 2 (2032), 1, 1, 1, 2 (2036), and so on. The cumulative shift first reaches a multiple of 7 at 2037 after 11 years: 11 plus 3 leap days (2028, 2032, 2036) equals 14, which is 0 mod 7, and 2037 is a common year. So the answer is **2037**; a program scan of 2027 to 2099 confirms nothing earlier matches.
Source: Calendar-repeat reasoning is a standard recreational topic; this instance written for AxiomIQ.