Three portions of cheese

The Workings

We have a new divertimento of culinary sharing. As we already said in Balanced division of a sandwich, “balanced divisions are often far from being innocent problems, especially if issues of economic redistribution and political interplay underlie them”. Today we are concerned with the distribution of a cheese that has already been cut into pieces over whose weight there are discrepancies; perhaps it would have been better if they had shared a good Torta del Casar… although that has also been bringing about other kinds of discrepancies.

The Fun

Three friends buy a cheese weighing 1800 g. The first of them cuts it into three pieces. The second decides to weigh the pieces on a scale in the shop, which shows weights of 500 g, 600 g and 700 g. The third decides to reweigh the pieces on a scale at home, which shows weights different from those on the scale. When they go to divide up the pieces, they disagree: the first friend insists that the pieces he cut are the same, the second claims that the shop’s scales work correctly, and the third claims that the scales at home show the real weights. How should they divide up the pieces of cheese, without cutting them up again, so that everyone believes that their piece weighs at least 600 grams?

 

 

 

 

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.