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# Who served first?

## Question

Araver beat plasmid in a set of tennis, winning six games to plasmid's three.
There were five service breaks (games in which the serving player lost.)

Who served the first game?

## Recommended Posts

• 1

Araver serves first. There are 9 games played. If they alternate first serves, plasmid will serve either 4 or 5 times. If it's 4 serves, to win 3 games, the (serves lost, receptions won) combinations would be (1,0) (2,1) (3,2) and (4,3). For 5 serves, it would be (2,0) (3,1) (4,2) and (5,3). Since each of the (serves lost, receptions won) is a service break, for (a,b), a+b must equal 5. The only combination fitting this is (3,2) under 4 serves for plasmid meaning Araver has 5 and serves the first game.

Edited by Thalia

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