KöMaL 2025 C1862

$n$ (${>2}$) children want to play on the two undistinguishable swings of the playground. They have decided that everybody will play together with two other children for two minutes. After each round, the two children have to hand over the swings to another pair who have not yet played on the swings together. (A child handing over the swing to the next pair cannot be in the next pair.) Is the plan of the children feasible?