Connecting three houses to three utilities

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When I was a child I was given this problem to send a wire from electricity, water, and internet to each of the houses, all three houses must have all three wires connected without being crossed over each other (wires can't meet and there is no such thing as a wire going on top of another wire) , I have always gotten to the point where I can connect all but except one wire.

Now after many years this just came to my mind today, and I wanted to ask why isn't it actually possible? What makes the last wire so special? That u can't connect the 9th wire in a 2D plane. Let me know if anyone know how to solve it or if anyone knows a proof (in layman terms) as to why it's Impossible.