[Mathematical logic (miscellaneous).]

The first Tuesday of the month Mitya spent in Smolensk, and the first Tuesday after the first Monday - in Vologda. In the following month Mitya spent the first Tuesday in Pskov, and the first Tuesday after the first Monday - in Vladimir. Can you determine the date and month when Mitya was in each of the cities?

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Why did the month in which Mitya was in Smolensk and Vologda start on a Tuesday?

## Solution

Since Mitya could not spend the same day in both Smolensk and Vologda, the month must have started on a Tuesday (otherwise, the first Tuesday and the first Tuesday after the first Monday would coincide). Similarly, we conclude that the second month must also start on a Tuesday. This is only possible if one month is February and the other is March, and the year is not a leap year. From this, it is easy to determine that Mitya was in Smolensk on February 1, in Vologda on February 8, in Pskov on March 1, and in Vladimir on March 8.

## Answer

In Smolensk - February 1, in Vologda - February 8, in Pskov - March 1, in Vladimir - March 8.