The peculiarities of tennis throw up some nice problems. When better to ponder them than on the opening day of Wimbledon?
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?
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?
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.)
I’ll be back at 5pm with the solutions.
PLEASE NO SPOILERS. Instead suggest your favourite tennis-based puzzles.
I set a puzzle here 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.
I’m the author of Football School, a book series for 7 to 12 year olds that opens up the curriculum through football. Football School Star Players: 50 Inspiring Stories of True Football Heroes is just out. It profiles 50 footballers – including Women’s World Cup heroes Lucy Bronze and Megan Rapinoe – who show that football can be a force for good both on and off the pitch.
Sources for today’s puzzles: Dick Hess, Number-Crunching Math Puzzles; Frederick Mosteller, Fifty Challenging Problems in Probability; Paul Vaderlind, The Inquisitive Problem Solver.