January 1, 1995 was a Sunday. What day of the week lies on January 1, 1996 ?

Concept: An ordinary (non-leap) year has 365 days. Since 365 = 52 x 7 + 1, an ordinary year leaves exactly one odd day, so the same calendar date moves forward by one weekday from one year to the next. A leap year has 366 days = 52 x 7 + 2 and therefore leaves two odd days.

Application:

1. The span asked about runs from 1 January 1995 to 1 January 1996, which covers the whole of the year 1995.

2. 1995 is not divisible by 4, so 1995 is an ordinary year of 365 days.

3. Divide by the length of a week: 365 = 52 x 7 + 1, so the span carries 1 odd day.

4. Advance the given weekday by 1 odd day: Sunday + 1 = Monday.

5. Hence 1 January 1996 falls on Monday.

Cross-check:

• The leap day 29 February 1996 lies after 1 January 1996, so 1996 being a leap year does not affect this span; only the length of 1995 matters.

• Applying the same rule to the next span: 1996 is a leap year (2 odd days), so 1 January 1997 = Monday + 2 = Wednesday, which matches the actual calendar and confirms the odd-day method.