A cooperative has 5 sites with the following known distances (the distances are understood to be between the entrances of the sites): From Almás, Bárkány is 2 km away, from there Cseresznye is $1650 \mathrm{~m}$ away. From Cseresznye to Dinnye, the distance is 8 and a half km, and from there to Epres, it is 3 and $3 / 4 \mathrm{~km}$. Finally, from Epres to Almás, it is 1100 m. How far is it from Epres to Bárkány?
Among the given distances, the largest is equal to the sum of the others: $8500=1650+2000+1100+3750$. This is only possible if the 5 settlements are arranged in a straight line. The order of the points, moving in one direction, is: $C s, B, A$, $E, D$. From this, we can calculate the distance between any two settlements. The requested $E B$ distance is $1100+2000=3100$ meters.

![](https://cdn.mathpix.com/cropped/2024_05_02_8fd0317f56dd85dbe3b1g-1.jpg?height=127&width=550&top_left_y=305&top_left_x=777)

Agnes Molnar (Budapest - Cinkota, 12-year-old school 1st grade)