Nazarov $\Phi$.

15 elephants are standing in a row, each weighing an integer number of kilograms. If you take any elephant except the one on the far right and add twice the weight of its right neighbor, the result is 15 tons (for each of the 14 elephants). Find the weight of each of the 15 elephants.
Number the elephants from left to right from 1 to 15. Denote the weight of the elephant with number $i$ as $5000 + x_{i}$ kg ($i=1, \ldots, 15$). Then $\left(5000 + x_{i}\right) + 2\left(5000 + x_{i+1}\right) = 15000$, which means $x_{i} = -2 x_{i+1}$. Therefore, $x_{1} = -2 x_{2} = 2^{2} x_{3} = -2^{3} x_{4} = \ldots = 2^{14} x_{15}$.

If $x_{15} > 0$, then $x_{15} \geq 1, x_{1} \geq 2^{14} = 16384$, and the weight of the first elephant exceeds 15 tons. Similarly, we reach a contradiction if $x_{15} < 0$. Therefore, $x_{15} = 0$, which means $x_{1} = x_{2} = \ldots = x_{15} = 0$, and the weight of each elephant is 5 tons.

## Answer

The weight of each elephant is 5 tons.