Winning bets

One of the "charts" in youtube is the following video showing how to win bets. There is some interesting mathematics involved because many math problems have surprising moves. A prototype is to give somebody 6 matches and ask to arrange them to build 4 triangles each with the side length of a match. Everybody will of course look to build it in the plane and fail because it is impossible: with f=4 triangles and e=6 edges, the Euler polyhedron formula v-e+f = 2 shows that v=4. We need 4 vertices and it is impossible to build that in the plane with the length constraints given. One has therefore to go into space and build a tetrahedron. One can consider it hair splitting or "trick" but often counter examples to things which are obvious are "tricks". And once, a trick is used a second time, it is no more a trick, but a "method". One can learn a lot by collecting "methods". The principle goes deeper in science. There were many examples, where scientists or engineers have "proven" something to be impossible. But then it was possible too. An example is to build a rocket lifting a mass to space. It became possible because rockets used different stages (a "trick"). But here is the movie:


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