Question

There are 256 players in a chess tournament (singles). Two players play a match. Matches are played on a knockout basis, the loser is eliminated after each match. How many matches need to be played to declare a winner? There is no draw.___

Answer 1

For two players, we need one match. The first round, having 256 players will need $\frac{256}{2}$= 128 matches.

Now there are 128 players left. To ensure that all players play a match, we need $\frac{128}{2}$= 64 matches

Continuing in the same way

Total number of matches = 128+64+ 32+ 16+8+4+2+1= 255

OR

In 1 match 1 player is eliminated

For tournament to conclude there should be only 1 winner and hence 255 players need to lose.
Hence we need 255 matches to eliminate 255 players.