[Mathematical logic (miscellaneous).]

Teams A, B, V, G, and D participated in a relay race. Before the competition, five fans made the following predictions.

1) Team D will take 1st place, Team V - 2nd;
2) Team A will take 2nd place, 2-4th
3) V - 3rd place, D - - -th
4) V - 1st place, G - 4th;
5) A - 2nd place, V - 3rd.

In each prediction, one part was correct, and the other was not. What place did each team take?
From 1) it follows that there are two cases.

1. D took 1st place. Then from 3) it follows that B took 3rd place, further from 5) it follows that A did not take 2nd place, and then from 2) it follows that $\Gamma$ took 4th place. For A and B, the remaining places are 2nd and 5th, so A took 5th place.
2. B took 2nd place. Then in prediction 5) there are no correct assumptions. Contradiction.

## Answer

Teams in the order of places taken: D, B, V, G, A.