Which is the next year after 2026 whose calendar is exactly the same as the calendar of 2026, so that every date falls on the same day of the week?

Two things must match: the starting weekday and whether the year is a leap year. Each ordinary year pushes the next year's starting weekday on by 1 day and each leap year pushes it on by 2. Adding those pushes from 2026 onwards gives running totals of 1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 14 by the start of 2037 — and 14 is a whole number of weeks. Since 2026 and 2037 are both ordinary years, their calendars match exactly. The traps: 2032 does start on the same weekday (a running total of 7), but it is a leap year, so from March onwards every date slips; 2031 comes from the half-remembered folk rule that a calendar repeats every five or six years; 2038 is one year past the right answer and starts a day later.