The international school had a conference these past two days. I gave a talk on "enquiry maths". One of the parents did a problem solving talk that had a very nice finish. The problem: cut a cake into 8 equal pieces with 3 cuts.
The classic solution is to quarter the cake in the regular way and then make a horizontal cut through the middle. After this solution was offered, the speaker produced a cake and a knife and asked for a demonstration. Of course with the frosting and the marzipan flowers on top, the pieces were anything but equal.
After some hemming and hawing, someone came up with another solution. Cut the cake into quarters and then stack them, making a final cut dividing them into equal slices. Again, he produced a cake and asked for a demonstration. After the stacking, the flowers were crushed and the pieces looked horrible.
Another solution? At last, someone suggested lining the slices up on the table and making a very long cut through them. The problem is that that's a tricky cut to make, unless you have... a sword! He pulled out a sword and finally we had a wonderful solution.
It was a well-planned demonstration of the difference between mathematical and practical solutions, and a perfect marriage of the two.