Today’s puzzle appeared in last year’s British Mathematical Olympiad (BMO), a competition taken by almost 2,000 school pupils in the UK.
The BMO is the top national maths contest for pre-university students, and is part of the selection process for the British team at the International Mathematical Olympiad and the European Girls’ Mathematical Olympiad.
Today’s question was one of the easier ones on last year’s paper. It was attempted by more than 90 per cent of entrants, and about 1 in 3 got full marks. Your serve…
Ping pong percentages
Arun and Disha played several games of table tennis. At five points during the day, Arun calculated the percentage of the games played so far that he had won. The results of these calculations were exactly 30 per cent, exactly 40 per cent, exactly 50 per cent, exactly 60 per cent and exactly 70 per cent, but not necessarily in that order.
What is the smallest possible number of games they played?
Here’s a hint (that wasn’t given to the BMO contestants.) Arun wins one of the first two games.
I’ll be back at 5pm UK with the solution. Meanwhile, NO SPOILERS!
UPDATE: To read the solution click here.
As mentioned above, the BMO is part of the process that selects the UK’s six-person team for the International Mathematical Olympiad (which this year takes place in July in Oslo) and the four-person team for the European Girls’ Mathematical Olympiad (EGMO), which took place in Hungary last month.
EGMO aims to increase female participation in the otherwise extremely male-dominated world of maths olympiads, and despite its name attracts teams from across the globe. In Hungary, the UK came 14th out of a total of 57 that took part. (Top of the rankings were USA, Peru, Australia, Romania and Bulgaria.) The UK team’s star member, Eleanor MacGillivray, who attends King’s Ely school, was the highest-scoring European contestant. Well done Eleanor!
The UK Mathematics Trust organises the BMO, as well as many other school maths competitions. For more information, please go to ukmt.org.uk.
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 several books of puzzles, most recently the Language Lover’s Puzzle Book. I also give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.
