Balanced division of a sandwich

The Workings

Today’s divertimento is quite innocent – it’s about sharing out a sandwich in a balanced way. But balanced distributions are often far from innocent problems, especially if issues of economic redistribution and political interplay underlie them. I recall what the former Socialist minister Josep Borrell said in this regard in a lecture he gave in the Andalusian Parliament in 2000 on the occasion of the World Mathematics Year. Borrell recounted what happened at a meeting in the late 1980s with representatives of the Basque Government to set the amount of the quota; in essence, the quota is the amount that the Basque Country has to pay each year to the State for the services it provides for non-transferred competences, and it is an example of a balanced distribution calculation with economic and political implications. Borrell and his team, politicians but with a strong scientific background – Borrell is, among other things, an aeronautical engineer, has a PhD in economics and a Master’s degree in Operations Research from Stanford University – tried to pose the calculation as an optimisation problem: “We are going to define the quota as a function that depends on a set of variables, the GDP of the Basque Country with respect to the GDP of the rest of Spain, the population, the tax effort, and try to model how this function should behave, to give it a value that is politically consistent,” explained Borrell. The representatives of the Basque Government looked at him and said: “Is this a joke or what?” According to Borrell: “The negotiation ended up badly, and I don’t want to tell you how the Basque quota was set, but it would not be easy to find a function that would provide a rational explanation for it”. To what Borrell said at the time, it should be added that the Basque Nationalist Party’s support for Mariano Rajoy’s latest budget meant compensation from the State of 1.4 billion euros for the settlement of the quotas for the last ten years.

The Fun

A sandwich is in the shape of an isosceles right triangle. It is to be cut into two pieces by a single straight cut, so that the two resulting figures have the same area. How should it be cut so that the cut is as short as possible?

 

 

 

 

Solutions

We encourage the readers to try to solve the divertimento for themselves. Whether you succeed or not, you can always consult the solution in this link.

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