Authors: Volchenkov S.G., Bogdanov I.I.
Nine skiers left the starting point one after another and covered the distance - each at their own constant speed. Could it have turned out that each skier participated in exactly four overtakes? (In each overtake, exactly two skiers participate - the one who overtakes and the one who is overtaken.)
Suppose this happened. Since the speeds are constant, each pair of skiers met no more than once. The skier who started first could not overtake anyone; therefore, four people overtook him, and he finished fifth. On the other hand, the skier who started last could not be overtaken by anyone, so he himself overtook four people and also finished fifth. Contradiction.
## Answer
It could not have happened.