# Did you solve it? Ace these tennis teasers

Earlier today I set you the following puzzles.

1) Ashleigh Barty and Naomi Osaka are playing a set of tennis. In the last eight points, Barty has served seven aces and Osaka has served one. What’s the score?

Solution

Barty is ahead 2-1 in the tiebreak.

Barty was 5-6 down, and 0-40 down. She scored five aces to get to the tie-break, then Osaka served an ace, then Barty hit another two aces.

2) Let’s say Wimbledon abolishes seeds, and each of the 128 players in the men’s singles is assigned a position in the first round grid at random. And let’s assume that the best player will beat everyone, and that the second-best player will beat everyone except the best player. What are the chances that the second-best player is the championship’s runner-up?

Solution

64/127

For this outcome, all that needs to happen is for the best and second-best players to be in different halves of the draw. Let’s say that the best player is one half. For the second-best player to be in the other half, he can be in 64 out of the remaining 127 positions in the grid.

3) Novak Djokovic and Roger Federer are playing in the Wimbledon final. Djokovic wins the first set 6-3. If there were 5 service breaks in the set, who served the first game? (A service break is a game won by the non-server. Service changes with each game.)

Solution

Djokovic.

If there were 9 games in the set, then one player served 4 games and one served 5. Let’s assume that Djokovic served 4 games and Federer served 5 games. Let’s also say that Federer had k service breaks, meaning that he lost k of his 5 service games.