# The first round of the 2010 FIFA World Cup consisted of several groups of four teams each. Within each group, each of the four teams played each other once. How many matches were there in each group?

May 9, 2018

$6$

#### Explanation:

So let's use Group C as an example:

• USA
• Algeria
• England
• Slovenia

Here are all the matches that need to be played
(I've color-coded the teams so you can tell them apart easier):

1. $\textcolor{b l u e}{\text{USA}}$ v. $\textcolor{g r e e n}{\text{England}}$
2. $\textcolor{red}{\text{England}}$ v. $\textcolor{\mathmr{and} a n \ge}{\text{Slovenia}}$
3. $\textcolor{b l u e}{\text{USA}}$ v. $\textcolor{red}{\text{England}}$
4. $\textcolor{g r e e n}{\text{Algeria}}$ v. $\textcolor{\mathmr{and} a n \ge}{\text{Slovenia}}$
5. $\textcolor{b l u e}{\text{USA}}$ v. $\textcolor{\mathmr{and} a n \ge}{\text{Slovenia}}$
6. $\textcolor{g r e e n}{\text{Algeria}}$ v. $\textcolor{red}{\text{England}}$

At this point, every team has played every other team exactly once.