Here is a quick cake conundrum for you.
Two girls are decorating the christmas cake. It is a square fruit cake. They share the icing such that one girl ices the top and one face. The other girl ices the remaining three faces. What possible dimensions of the cake will make the icing areas equal?
I spotted this ‘Expert Tip’ whilst flicking through a supermarket magazine:
Image credit: tesco.com/foodandliving
Question
If this cake has a diameter of 18cm (7in), is this a fair way to split it between guests? Can you prove your result in general terms?
Of course, this assumes that the icing on the side doesn’t count in the diameter or guest preference.
There was an interesting discussion on the BBC Breakfast programme this morning about the exchange of maths teaching ideas between British and Chinese teachers.
The guests on the sofa were from the NCETM and a serving Head of Maths. There was mention of the innovative ideas used to teach Maths in Britain – including some of mine. I’m not being presumptive, I happen to know that Head of Maths – in fact some of his ideas are on this site (JDs Tree Diagrams). So just in case you missed Breakfast, here is some Cake.