Grades 7-8 Video Solutions 2021-video 2021 7-8/29

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Question 29. In a tournament, each of the six teams plays one match against each of the other teams. In each round, three matches take place simultaneously. A TV  station has already decided which match it will broadcast for each round, as shown in the diagram. In which round will Team D play against Team F? So if we  draw the way that the teams will be broadcasted, we have to recognize that teams are playing at the same time. So a team can't play on the same day twice. If  we take a look, we have Team A fighting Team B, Team A fighting Team C, Team A fighting Team E, but we don't have Team A fighting Team D or A fighting Team F.  So we can begin by putting in Team A fighting Team D on day four, since we know that this is the only applicable day where these two teams could fight.  Likewise, we can put A and F on day two, since this is the only day that A isn't fighting in or F is fighting in. Next, we can have Team C and E fight each other  on day one, and then Team C and F fight on day three. After this, since all the other days have Team C fighting except for day four, we will have day four C and  B fight, after which we can look at the combinations of teams D and E and recognize that they will have to fight on day five. With this, we have enough  information to know where to place Team D and F, since day two already has Team D and F both fighting separate teams, day three has Team F fighting, day four has  both F and D fighting other teams, and day five has D fighting a team. We know that D and F will have to fight on day one, so our answer is A, one.

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