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.

The number of service games that Federer won is therefore 5 – *k*. Since there were 5 service breaks in total, the number of Djokovic’s service breaks is also 5 – *k*. Furthermore, Federer wins Djokovic’s service breaks, so the total number of games won by Federer is 5 – *k *+ 5 – *k* = 10 – 2*k*.

We know that Federer won 3 games. But there is no solution for *k *in which 10 – 2*k = *3, since *k *is a whole number. We are led into a contradiction, so our assumption that Djokovic served four games, and Federer five, must be wrong. Djokovic must have served five games, and thus he served the first game.

I hope you enjoyed today’s puzzles and I’ll be back in two weeks.

*I set a puzzle every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.*