Math kangaroo level 5-6

[varshadongre]

In a basketball tournament 32 teams are competing. At each stage the teams are divided into groups of 4. In each group every team plays once against every other team. The best two teams are qualified for the next round. The other two teams are eliminated. After the last stage the two remaining teams play one final match to determine the winner. How many matches will be played in the whole tournament?

 

[varshadongre]

Need help to solve this problem

 

[Deleted member 4993]

In a basketball tournament 32 teams are competing. At each stage the teams are divided into groups of 4. In each group every team plays once against every other team. The best two teams are qualified for the next round. The other two teams are eliminated. After the last stage the two remaining teams play one final match to determine the winner. How many matches will be played in the whole tournament?

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[Steven G]

Need help to solve this problem

I agree with that 100%. So where are you stuck?

 

[HallsofIvy]

In a basketball tournament 32 teams are competing. At each stage the teams are divided into groups of 4.

So there are 32/4= 8 such groups.

In each group every team plays once against every other team.

Each of the four teams plays each of the three other teams. Since each game involves two teams that is 4(3)/2= 6 games per group. There are 8 groups so 8(6)= 48 games.

The best two teams are qualified for the next round.

I presume you mean the best two teams in each group.

The other two teams are eliminated.

So there are 8(2)= 16 teams left. Dividing those into groups of 4 there will be 4 groups. Again there are 6 games per group so 4(6)= 24 games in this round. Keeping the best two from each group leaves 4(2)= 8 teams. Now dividing into groups of 4 gives two groups. Again there are 6 games per group so 2(6)= 12 games in this round. Keeping the best two from each group now leaves 4 teams. There will be, again, 6 games in this round. That leaves two teams which play each other once.

After the last stage the two remaining teams play one final match to determine the winner. How many matches will be played in the whole tournament?

Now that you know the number of games in each round, how many games are the altogether?