In a cricket championship, there are 21 matches. If each team plays one match with every other team, the number of teams is

Question

This is either a permutation or a combination question. I suspect it is a combination. Does it require using algebra because there is no n provided? Sorry, I am really weak on this topic. Thank you for helping out!!!

Answer 1

Suppose there are $n$ teams, call them Team $1,\ldots,n$. Now Team $1$ plays Team $2,\ldots,n$ (total of $(n-1)$ matches), Team $2$ plays Team $3,...,n$ (total of $(n-2)$ matches), and so on. So the total number of matches is $(n-1)+(n-2)+\ldots+1=21$.

$21$ is a small number and in this case you can see that since $1+2+3+4+5+6=21$, we have $n=7$.