Folkpor

Three pirates were dividing a bag of coins. The first took $3 / 7$ of all the coins, the second took $51 \%$ of the remainder, after which the third received 8 coins less than the second. How many coins were in the bag?
Since the second pirate took $51\%$ of the coins remaining after the first, the third pirate received $49\%$ of this amount. Therefore, 8 coins represent $2\%$ of the coins remaining after the first pirate. Thus, the share of the second and third pirates is $8 \cdot 50 = 400$ coins, which is $\frac{4}{7}$ of their total amount. Therefore, the bag contained $400 : \frac{4}{7} = 700$ coins.

## Answer

700 coins.

Author: Kovaldzhi A.K.

Vladimir runs on a circular track at a constant speed. There are two photographers standing at two points on the track. After starting, Vladimir was closer to the first photographer for 2 minutes, then closer to the second photographer for 3 minutes, and then closer to the first photographer again. How long did it take Vladimir to run the entire circle?

## Solution

Mark the first and second photographers on the circle with points $A$ and $B$ respectively, and points $C$ and $D$ to denote the midpoints of the arcs connecting $A$ and $B$. Then on the semicircle $C A D$, Vladimir is closer to the first photographer, and on the semicircle $C B D$ (marked in bold on the diagram) - closer to the second photographer. According to the problem, he was closer to the second photographer for 3 minutes. Therefore, he runs the entire circle in 6 minutes.

![](https://cdn.mathpix.com/cropped/2024_05_06_79aa1f75de69bad6c7b2g-13.jpg?height=386&width=395&top_left_y=613&top_left_x=840)

Answer

In 6 minutes.