A city is hosting a table tennis tournament for its residents. Each

So here initially total number of teams are 512/2= 256

So in round 1 256/2 = 128 matches will be played since after each of these 128 matches the loosing team will be eliminated so remaining would be 128

Subsequently in round 2- 128/2 = 64 matches will be played

in round 3- 64/2 = 32 matches will be played

in round 4- 32/2 = 16 matches will be played

So after round 4, 16 teams will be remaining

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We have 512 participants to be paired under a team of two who will play one match with the opposition team and losing team will be eliminated.

512 players = 256 teams (2*256=512)
One team is playing with other then 128teams vs. 128teams (1st round)
128 matches were played in first round.

Now, 128 losing teams are eliminated after first round.
So 128 teams will be divided in pair of 64 teams to play against each other.
64 vs. 64 (2nd round)
Similarly,
32 vs. 32 (3rd round)
16 vs. 16 (4th round)
8 vs. 8 (5th round)... And so on.

Now we have no. 2 4 8 16 32
=> Let say 32 teams were remaining, but 32 are remaining After 3rd round.
So 32 can't be the remaining team.
=> Let say 2 teams were remaining but 2 were remaining after 7th round which is also not an option.
=> Similarly if you put values in other combinations, you will find only 16 teams were remaining after 4th round. (The possible combination)

So the answer is 4th round and 16 teams.

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