39. In a chess tournament, each of the 8 participants plays one game with each other. All participants scored a different number of points (an integer), and the second-place finisher scored as many points as all the chess players who finished from fifth to eighth place combined. How did the players who finished in third and fifth place play against each other?
39. The participant who took second place, out of a total of 28 points scored by all participants together, scored no more than six points, as otherwise, they would have taken either first place or shared the first and second places, which contradicts the condition. The only possible scenario is: $28=7+6+5+4+3+2+1+0$. On the other hand, if the participants who took fifth through eighth place inclusive scored 6 points, then these points were earned by playing against each other, losing all games to the chess players who took the top four places. Therefore, the participant who took third place won against the one who took fifth.