In 2003 there are 28 days in February and 365 days in a year in 2004 there are…
2026
In 2003 there are 28 days in February and 365 days in a year in 2004 there are 29 days in February and 366 days in the year. If the date March 11 2003 is Tuesday, then how many odd days are present between 11 March 2003 and 11 March 2004?
- A.
2
- B.
3
- C.
9
- D.
5
Attempted by 3 students.
Show answer & explanation
Correct answer: A
An 'odd day' is the remainder left when the total number of days in a span is divided by 7, since every complete block of 7 days brings the calendar back to the same day of the week. An ordinary 365-day year always leaves 1 odd day (365 = 52×7 + 1), while a leap 366-day year always leaves 2 odd days (366 = 52×7 + 2).
Applying this to the given span:
The interval runs from 11 March 2003 to 11 March 2004 — a full 12-month span.
Although 2003 is not a leap year, this particular span crosses 29 February 2004, because 11 March 2004 falls after that leap day. So the span includes the leap day and therefore contains 366 days, not 365.
Divide 366 by 7: 366 = (52 × 7) + 2, i.e. 52 complete weeks plus a remainder of 2.
So the number of odd days between 11 March 2003 and 11 March 2004 is 2.
Cross-check using the given day of the week: 11 March 2003 is a Tuesday. Shifting Tuesday forward by the interval's odd-day count of 2 gives Thursday, so 11 March 2004 falls on a Thursday — consistent with a leap-affected span moving the weekday by 2 days rather than the 1 day a non-leap 365-day span would give.
