A2. Today is February 4, 2011. This date is written as 04-02-2011. In this problem, we look at the next day whose date is written with eight different digits. In which month does this day fall?
A) January
B) March
C) June
D) October
E) December
A2. C) June The year of the sought date starts with a digit that is 2 or higher. We are looking for the first date where the year starts with a 2 and all eight digits are different. If it exists, it is the sought date.

For the month, 11 (two identical digits) and 12 (digit 2 is already used in the year) are ruled out. The month (01 to 10) therefore contains the digit 0. The day thus starts with either a 1 or a 3. In the latter case, it is the 31st, as the 0 is already occupied. In both cases, the 1 is in the day. Now that 0 and 1 are already occupied, the smallest possible year is 2345. The smallest possible month we can then choose is 06, or June, with the day being the 17th. We see that the found date, 17-06-2345, is indeed written with eight different digits.