Question

In the chess championship, $153$ games have been played. If a player with every other player plays only once, then the no. of players are?

• A. $17$
• B. $51$
• C. $18$
• D. $35$

Answer 1

The correct option is C

$18$

Explanation for the correct option:

Finding the number of players:

Number of players requires in chess $=2$

Total number of games $=153$

Let the required number of players be $n$ then

$$\begin{gathered} \Rightarrow {}^{n}C_2=153 \\ \Rightarrow \frac{n(n-1)}{2}=153 \\ \Rightarrow n(n-1)=306 \\ \Rightarrow n^2-n-306=0 \\ \Rightarrow n^2-18n+17n-306=0 \\ \Rightarrow (n+17)(n-18)=0 \\ \Rightarrow n=18orn=-17 \end{gathered}$$

Here $n=-17$is not satisfied so$n=18$ be the required number of payers

Hence, option C is the correct option.