## October 13, 2008

### Reasoning Puzzles

97 baseball teams participate in an annual state
tournament. The champion is chosen for this
tournament by the usual elimination scheme. That is,
the 97 teams are divided into pairs, and the two
teams of each pair play against each other. The
loser of each pair is eliminated, and the remaining
teams are paired up again, etc. How many games must
be played to determine a champion?

Secret SquÃ¯rrel said...

The odd number (97) of teams is a furphy designed to muddy the waters ("how do we treat the odd team - do they get a bye to the next round or do they have to play one of the others who have already played?")

However, when you realise that each game only ever eliminates 1 team, and that 96 teams must be eliminated in order to determine a champion from 97, then you know that, no matter what the format, you must play 96 games.

satish said...

96

rahul kolla said...

86 games

Anonymous said...

tash....

consider 17 teams.

they can be diced into 8 groups and 1 extra team. so 8 games are played and 8 teams are eliminated.
total matches=8

now 9 groups are diced into 4 groups and 1 extra team. 4 matches are played and 4 teams eliminated.
total matches=8+4=12

now there are 4 winner teams and the extra team. they are diced into 2 groups and an extra team.
they play 2 matches and 2 winners emerge.
total number of games= 8+4+2=14

now 2 winners and an extra team are there. so 2 teams play and an extra team is kept aside.
number of matches= 8+4+2+1=15

the winner of the previous game and the extra group play and there is only one winner.
number of matches-8+4+2+1+1=16

the extra group can be the group with highest scres or arbitarily decided.

it works similarly for 97 groups.so answer is 96.