Plus Blog

July 26, 2012

Yesterday we brought you two Olympic brainteasers. Here are another two. Enjoy!


Fencing Tournament

Alice, Becky, Charlotte, Daphne, Elsie and Fran decide to compete in a fencing tournament. Each competitor has to fence against every other competitor. A match results in either a win or a loss.

  • No competitor lost all their matches, but one person won all their matches.
  • Daphne won her match against Becky.
  • Alice and Elsie won the same, odd, number of matches, but Alice lost to Elsie.
  • Becky and Fran won a total of seven matches
  • Charlotte won only one match, against the only other person who also won only one match.

Can you deduce what all of the results were?


In a hockey competition, four teams were to play each other once. 2 points were awarded for a win, and 1 point for a draw.

After some of the matches were played, most of the information in the results table was accidentally deleted.

Team Played Won Drawn Lost For Against Points
A 4 4
B 5 5
C 0 4 2
D 0 3 0

Can you work out the score in each match played?

These brain teasers come from our sister site NRICH, which also has detailed teachers notes for them.

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July 25, 2012

While the athletes are flexing their muscles, why not train your brain with these two Olympic puzzles? There'll be another two tomorrow.

Medals Count

Given the following clues, can you work out the number of gold, silver and bronze medals that France, Italy and Japan got?

  • Japan has 1 more gold medal, but 3 fewer silver medals, than Italy.
  • France has the most bronze medals (18), but fewest gold medals (7).
  • Each country has at least 6 medals of each type.
  • Italy has 27 medals in total.
  • Italy has 2 more bronze medals than gold medals.
  • The three countries have 38 bronze medals in total.
  • France has twice as many silver medals as Italy has gold medals.

Football Champ

Three teams A, B and C have each played two matches.

Three points are given for a win and one point to each team for a draw.

The table below gives the total number of points and goals scored for and against each team.

Fill in the table and find the scores in each match.

Teams Games Played Won Drawn Lost Goals For Goals Against Points
A 2 5 3 3
B 2 2 1
C 2 3 2 4

These brain teasers come from our sister site NRICH, which also has detailed teachers notes for them.

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July 24, 2012
Usain Bolt

Can you out run Bolt? Image: Jmex60.

What can you do to out sprint Usain Bolt to the taxi rank? Was he unlucky to lose at the Jamaican trials or is Yohan Blake really faster? Get in training for a summer of sport with a talk from John D. Barrow at the Science Museum tomorrow, 25th July. The talk is part of an evening dedicated to science and sport, part of the Science Museum Lates series. You'll also be able to test out the devices helping to keep athletes' bones in top condition, from hand-held scanners to vibrating platforms, and be part of the Science Museum sports day with a variety of thrilling events. The evening starts at 6:45pm and finishes at 10:00pm and all events are free. See the Science Museum website for more information.

John D. Barrow is the director of the Millennium Mathematics Project, of which Plus is a part, and he regularly writes for Plus, often on maths and sport. You can see all his articles here. Also, don't forget our sister site Maths and sport: Countdown to the Games and our teacher package on maths and sport.

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July 24, 2012

Are you ready for the Games? Andy Murray passes the Olympic Flame to Venus Williams at Wimbledon on the 66th day of the torch relay.

Will Britain be able to turn the home advantage into the top spot on the medal table this Games? Predicting medal counts is a tricky business, but, never afraid of a challenge, we will reveal our own predictions for the top 20 countries here on Plus on Friday. In the meantime, why not come up with your own mathematical method for predicting the results? To help you along, here are two articles we produced for the 2008 Games in Beijing:

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July 23, 2012

Only four days to go until the start of the London 2012 Olympic Games! To get into the spirit, we cast our minds back to one of our favourite features of the 2008 Beijing Games: the beautiful aquatics venue, known as the water cube. Looking like it's been sliced from a giant bubble foam, the design is based on an unsolved maths problem. And although the bubbles look completely random, the underlying structure is highly regular and buildable. Find out more about this beautiful building in our article Swimming in mathematics.

The Water Cube at night

The Water Cube at night. Image © Chris Bosse.

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July 17, 2012

Henri Poincaré died 100 years ago today.

Henri Poincaré died 100 years ago today. He is most famous for the conjecture (now theorem) which carries his name and which remained open for almost 100 years, until Grigori Perelman announced a proof in 2003. But the conjecture isn't all there was to Poincaré. One of his teachers reportedly described him as a "monster of maths" who, perhaps because of his poor eyesight, developed immense powers of visualisation, which must have helped him particularly in his work on geometry and topology. He has been hailed one of the last people whose understanding of maths was truly universal. And he also thought about the philosophy of mathematics. He believed that intuition has an important role to play in maths, and anticipated the work of Kurt Gödel, who proved that maths cannot ever be completely formalised. Finally, and extremely pleasingly for us here at Plus, Poincaré was one of the few scientists of his time to share his knowledge by writing numerous popular science articles.

You can find out more about the Poincaré conjecture and related maths in these Plus articles:

And there is more on Poincaré's life and work on the MacTutor history of maths archive.

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