Task 2. Amir is 8 kg heavier than Ilnur, and Daniyar is 4 kg heavier than Bulat. The sum of the weights of the heaviest and lightest boys is 2 kg less than the sum of the weights of the other two. The total weight of all four is 250 kg. How many kilograms does Amir weigh? (20 points)
Answer: 66 kg.

Solution. Let the weight of Bulat in kilograms be denoted by $x$, and the weight of Ilnur by $y$. Then Amir weighs $y+8$, and Daniyar weighs $-x+4$. Note that the heaviest is either Amir or Daniyar, and the lightest is either Ilnur or Bulat.

If the heaviest is Daniyar, then $x+4>y+8$, so $x>y$ and the lightest is Ilnur. In this case, the combined weight of the heaviest and the lightest is $x+4+y$, which is 4 kg less than the combined weight of the other two. This is a contradiction. Therefore, the heaviest is Amir.

Suppose Bulat is the lightest. Then together with Amir, they weigh $x+y+8$, which is 4 kg more than the other two boys. This is a contradiction.

The only remaining case is when the lightest is Ilnur. In this case, Ilnur and Amir together weigh $2y+8$. From the problem statement, it follows that Bulat and Daniyar together weigh $2y+10$. Therefore, the total weight of all four boys is $4y+18=250$, from which $y=58$. Therefore, Amir weighs 66 kg.

Criteria. Only the correct answer with an incorrect or missing solution -3 points. Missing cases during enumeration - no more than 10 points depending on the number and severity of the missed cases.

In the case of a solution like the jury's, missing any of the first two cases (with the rest of the solution correct) - 10 points; missing both of the first two cases with the third case correctly analyzed - 6 points.