Priya bought a 2023 wall calendar with photographs she loved. In which year will she first be able to hang it up again with every date on the correct day?

Explanation

1. 01

   The later year must start on the same day as 2023 (a Sunday) and must also be an ordinary year.

2. 02

   Add odd days year by year: 2023 gives 1, 2024 gives 2, 2025–2027 give 1 each, 2028 gives 2, 2029–2031 give 1 each, 2032 gives 2, 2033 gives 1. Running total after 2033: $1+2+1+1+1+2+1+1+1+2+1 = 14$, a multiple of 7.

3. 03

   So 1 January 2034 is a Sunday, and 2034 is ordinary: the calendar repeats in 2034.