# Task 5.

Once upon a time, Baba Yaga and Koschei the Deathless tried to divide a magical powder that turns everything into gold equally. Baba Yaga took out a scale and weighed all the powder. The scales showed 6 zolotniks. Then she started removing the powder until the scales showed 3 zolotniks. However, Koschei suspected that the scales were lying and weighed the portion that had been removed separately on the same scales (there were no others). The scales showed 2 zolotniks. Determine the exact weight of the two parts into which Baba Yaga divided the powder. Assume that if the scales are lying, they always lie by the same amount.
# Solution.

Let $A$ be the weight of the first part (the one that remained on the scales), $B$ be the weight of the second part (the one that was poured off), and $d$ be the error of the scales.

Then the result of the first weighing (of the entire powder) gives

$$
A+B+d=6,
$$

the result of the second weighing (after pouring off) gives

$$
A+d=3
$$

and the result of the last weighing (of the poured-off part) gives

$$
B+d=2
$$

Adding the last two equations, we get

$$
A+B+2 d=5
$$

Subtracting the first equation from the obtained one, we get

$$
d=-1
$$

Thus, the scales reduce all readings by 1 zolotnik. From this, the answer immediately follows.

Answer: 4 and 3 zolotniks.