More or Less Brain Teaser

[Neill Cooper]

Problem set at the end of today's More or Less on Radio 4:

In a particular chess tournament, every contestant is supposed to play exactly one game against every other contestant. However, contestant A withdrew from the tournament after playing only ten games, and contestant B withdrew after just one game. A total of 55 games were played.
Did A and B play each other?
https://twitter.com/BBCMoreOrLess/statu ... 5345632257

From the 2015 Maths Olympiad for Girls Q4b (The answer to Q4a helps!)

[IM Jack Rudd]

A full eleven-player tournament is 55 games; a full twelve-player tournament is 66 games.

Thus, this tournament could be a 12-player tournament with eleven games missing. A has missed 1 of his 11 games; B 10 of his 11 games, which accounts for all our missing games. If A and B had not played, the same missing game would show up in both lists, and thus only 10 games would be missing. Thus A and B have played each other.

[Neil Graham]

On a totally different tack - where did the twitter photo come from?

One player appears to be smoking at the board; wooden chess pieces? It looks very 1970s to me.

[Kevin Thurlow]

White looks like Larry Christiansen, I think.

[NickFaulks]

This also raises the question of why there has to be a special Maths Olympiad for girls, in which the questions are insultingly easy. Girls can do maths.

[Mick Norris]

My daughter was recently part of the school team in the Maths Challenge locally - 2 girls 2 boys in each team

My impression from the evening was that possibly the girls were better than the boys (albeit not in my daughter's team, they just argued with each other and didn't win)

[MartinCarpenter]

The correct answer is actually undefined. It just says what should happen, but then gives two clear cut examples where it didn't happen and doesn't rule out any more.

I know this is pedantry but is it really too much to expect a maths Olympiad to have fully logically defined questions?

[Matthew Turner]

My daughter was recently part of the school team in the Maths Challenge locally - 2 girls 2 boys in each team

My impression from the evening was that possibly the girls were better than the boys (albeit not in my daughter's team, they just argued with each other and didn't win)

Every year I go to this competition and every year the staff sit around the hall for the final challenge. You naturally talk to the teacher next to you and I always end up saying "Isn't it interesting that more than half the competitors are female" (I cannot imagine that ever happening in chess) and every year I get the same response. "I hadn't noticed"

[Neill Cooper]

This also raises the question of why there has to be a special Maths Olympiad for girls, in which the questions are insultingly easy. Girls can do maths.

At the very top end the best school maths problem solvers are predominantly boys. This can be seen from the list of the top scorers in the British Maths Olympiad 2 sat in January this year. This challenge is very tough - only 34 UK students could gained more than 25% of the marks. Amongst the 34 are, I think, just 3 girls. Last year's International Maths Olympiad Teamwas 6 boys and no girls. I think the last time a girl was in the team for this annual competition was 2008.
It was for this reason that the the UKMT decided it had to develop girls' maths problem solving ability. So in 2011 they started the Maths Olympiad for Girls. That first year only 7 girls scored over 50% and it was decided that it was too tough. Over the years it has been made more accessible and this year 25 girls scored 90% or more. Perhaps the questions are now a bit too easy. But last week the girls team came 6th out of 31 European teams in the fifth European Girls’ Mathematical Olympiad, their best ever result.
It is great to hear coverage of the Girls Maths Olympiad on More or Less.

Edit to correct first link