Problem 4. Dima saw strange clocks in a museum (see figure). They differ from ordinary clocks in that their dial has no numbers and it is generally unclear where the top of the clock is; moreover, the second, minute, and hour hands are of the same length. What time did the clocks show?

![](https://cdn.mathpix.com/cropped/2024_05_06_611ab840a0f62c05d9afg-09.jpg?height=287&width=293&top_left_y=109&top_left_x=1032)

(The hands A and B in the figure are pointing exactly at the hour marks, while hand C is just a little short of the hour mark.)

[6 points] (D. E. Shnol)
Answer: Ten to five.

Solution: Let's think about which of the hands is the hour hand. If the hour hand were pointing exactly at an hour mark, the minute and second hands would be pointing exactly at the "12" mark - but there are no matching hands in the picture. Therefore, the hour hand must be hand B.

The remaining two hands are pointing exactly at hour marks, so it must be some number of hours and a whole number of minutes - in particular, the second hand is pointing at 12.

If the second hand is hand A, then it is just before seven o'clock (judging by the hour hand), but on the other hand, it is ten minutes past some hour (judging by the minute hand). This cannot be.

If, however, the second hand is hand B, then it is around five o'clock (judging by the hour hand), and according to the minute hand, it is ten minutes before some hour. Therefore, it is ten to five.