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Gas, water and electricity
In a suburb three new houses all have to be connected to a gas (red), water (blue) and electricity (green) supply. All houses should get their own gas, water and electricity connection. Furthermore no connections may cross each other. Because of the danger of stealing, no connections are laid below a house. In the figure on the right-hand side the situation is sketched. The red squares are the houses, the circles the point from which the connections should go to the houses.
Why is it impossible to lay down all connections in such a way that no connection crosses another connection?
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