Solution: Three portions of cheese

We publish the solution to the Three Pieces of Cheese divertimento.

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?

The Solution

We are going to let the last friend choose the one he prefers, the one that weighs the most according to the scales at home (as the three of them together weigh 1800 grams, at least one of them will weigh at least 600 grams). In the worst case, he will still leave one that weighs at least 600 grams according to the shop’s scale, which we can give to the second friend. Since the first friend thinks that all three weigh the same, whichever piece he takes, he will be happy, so he doesn’t cause us any trouble by keeping the one that his other two picky friends didn’t want.