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There are $5$ girls and $5$ boys in a chess club. The club holds a round-robin tournament in which every player plays against every other player exactly once.


In how many games does a girl play against another girl?

Respuesta :

Let's call the five girls [tex] g_1, g_2, g_3, g_4 \text {and } g_5 [/tex].


Since every player plays against every other player exactly once, [tex] g_1 [/tex] has to play against [tex] g_2, g_3, g_4 \text {and } g_5 [/tex]. This are four maches.


[tex] g_2 [/tex] has already played against [tex] g_1 [/tex], so she has to play against [tex] g_3, g_4 \text {and } g_5 [/tex]. This are three matches.


[tex] g_3 [/tex] has already played against [tex] g_1 \text{ and } g_2 [/tex], so she has to play against [tex] g_4 \text {and } g_5 [/tex]. This are two matches.


[tex] g_4 [/tex] has already played against [tex] g_1, g_2 \text{ and } g_3 [/tex], so she has to play against [tex] g_5 [/tex]. This is one match.


So, the total is [tex] 4+3+2+1 = 10 [/tex] matches.

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