Three friends, a mathematician, a physicist and an engineer, meet for dinner at a pizza place. The engineer arrives first and decides to order for everyone a 16″ stuffed crust pizza. The physicist arrives next and as the pizza is ready, states hating pizza crust and wishing to have as little as possible of that in his plate: but, he adds, I’ll pay 1/3 of the money, I want 1/3 of the area: that’s only fair. Right at this time the mathematician enters through the door. Discuss, in mathematical terms, the rest of the evening.

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Party cake

A classic USA math problem formulation involves sharing food fairly. Enjoy this problem with your lunch and the next one with your dinner 🙂

Five friends have ordered their favourite cake for a party. The cake is a parallelepiped and has icing on its top face and sides. Can you help our friends divide it fairly? Of course each friend needs to get equal amounts of cake, of top icing, and of side icing.

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Lenin and the subway

Comrade Lenin, as President of the Union of Soviet Socialist Republic, has lots of work to do, and his workdays finish late at night. Lenin has been married for decades with a comrade and activist, since the days of clandestinity, and loves her very dearly, they have shared everything and have built together a new world, and President Lenin would never divorce her. She has surely not become arrogant with power, and lives in a modest but dignified apartment. Comrade Lenin is, of course, not bound by the bourgeois morality and the contradictory bourgeois family structure, and he has a very attractive young girlfriend. She, too, is not corrupt with power and lives in a modest but dignified apartment not far away. Comrade Lenin, who is very scrupulous and very upright, has thought at length about the best arrangements, so that he should be fair to both, and they have found his suggestion a perfect solution. When he finishes working – at a random time in the evening – he walks from the Kremlin to the subway station, and boards the first train that arrives. According to the direction of the train, he will spend the night with his wife or his lover, because it happens that the two apartments are located on the same subway line, but one needs to take the train in opposite directions.

However, on average, in a month, he spends a night with his wife and the rest of the time with his attractive girl. How can this be?

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Two peasant ladies go to the market

It looks like nobody wants to be the first one to publish a post!

I’ll do, but the first post won’t be mine either. This is a problem I read somewhere in a book or article by V. I. Arnol’d.

Two peasant ladies leave simultaneously at dawn because they are going to a farmers’ country market: one lady leaves from town A and is going to B, while the other one is on her way from B to A. They walk at constant speed (each one at her own speed). At midday sharp, they greet each others without stopping and continue on their way.

At 16 (that is, 4 p.m.) the faster lady reaches her destination, and at 21 the other lady arrives, too.

Compute sunrise time.

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