January 1, 2008 is Tuesday. What day of the week lies on January 1, 2009 ?
Thursday
1 January 2009 was a Thursday — option 1.
Step 1 — how many days lie between the two dates ? From 1 January 2008 to 1 January 2009 is exactly the length of the year 2008.
Step 2 — is 2008 a leap year ? A year is a leap year if divisible by 4, except that a century year must be divisible by 400. Now
\(2008\div4=502\)
exactly, and 2008 is not a century year, so it is a leap year and has 366 days.
Step 3 — reduce to odd days.
\(366=7\times52+2\qquad\Rightarrow\qquad\text{odd days}=2\)
Step 4 — count forward. Two days after Tuesday :
Tuesday → Wednesday → Thursday
| Kind of year | Days | Odd days | Day advances by |
|---|---|---|---|
| Ordinary | 365 | 1 | One day |
| Leap | 366 | 2 | Two days |
The rule to carry away. The same calendar date advances by one weekday across an ordinary year and by two across a leap year. So 1 January 2007 was a Monday, 1 January 2008 a Tuesday, and 1 January 2009 — because 2008 was a leap year — a Thursday, skipping Wednesday altogether.
The trap. Treating 2008 as an ordinary year gives one odd day and the answer Wednesday, which is option 3 and is placed there for exactly that error. Note that the leap day, 29 February 2008, falls between the two dates, which is what makes the year in question the leap year rather than 2009.
Hence, the answer is Thursday.
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