[ Arithmetic. Mental calculation, etc.]

In an office with soundproof walls, there are old wall clocks that strike every half hour (one strike) and every hour (as many strikes as the hour hand indicates). Once, upon opening the door to the office, the owner heard one strike of the clock. Half an hour later, the clock in the office struck again - once again one strike. After another half hour - another single strike. Finally, another half hour later, the clock struck once again. What time did the clock show when the owner entered the office?
Think about the time of day when the clock will strike three times in a row, once every half hour.

## Solution

The clock will strike once every half hour, three times in a row, only at 12:30, 13:00, and 13:30. The fourth single strike can be heard by "catching" the last of the 12 strikes at 12:00. Therefore, when the owner entered the study, the clock showed 12:00.

## Answer

Exactly 12:00.

## Problem