2. Mom, dad, and nine children stood in a row on a straight path. Mom and dad are standing next to each other, 1 meter apart. Can the children stand in such a way that the total distance from all the children to mom equals the total distance from all the children to dad? If yes, provide an example; if no, explain why.
Answer. No.

Solution. Let the mother stand to the left of the father. Then the child standing to the left of the mother is 1 meter closer to the mother than to the father, and the child standing to the right of the father is 1 meter closer to the father than to the mother. For the sums of the distances to be equal, there must be an equal number of children standing to the left of the mother and to the right of the father. But the mother and father are standing next to each other, and nine children cannot be divided equally.

Comment. Correct solution - 20 points. It is noted that 9 children cannot be divided into equal groups, but there is no complete proof - 10 points. The solution is started, and there is some progress - 5 points. It is not taken into account that the mother and father are standing next to each other - 1 point. The solution is started, but the progress is insignificant - 1 point. The correct answer is given without explanation - 1 point.