Question

A huge Ping-Pong tournament is held in Beijing with 65,536 participants at the start of the tournament. Each round of

the tournament eliminates half the participants.
c. How many rounds of play will it take to determine the champion Ping-Pong player?

Answer 1

After 16 rounds the champion of Ping-Pong player can be determined.

Explanation:

This is an example of geometric progression,

First term = 65,536

`\texttt{Common ratio = }(1)/(2)`

Now we need to find which term is 1 in this GP.

N th term of GP is given by

`t_n=ar^(n-1)`

Substituting

`1=65536* \left ( (1)/(2)\right )^(n-1)\\\\(1)/(65536)=\left ( (1)/(2)\right )^(n-1)\\\\2^(n-1)=65536\\\\2^(n-1)=2^(16)\\\\n=17`

Seventeenth term of this GP is 1.

That is after 16 rounds the champion of Ping-Pong player can be determined.