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dodecahedron polyhedra

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$cool geometry and math art (fractals, tessellations, polyhedra and more)$

The Handshake Puzzle

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This brain bender is going to go in stages -- each getting harder than the last... See how far you can go!

Stage 1:	If you have TWO people in a room and each person shakes hands with every other person exactly once, how many total handshakes happen?
Stage 2:	If you have THREE people in a room and each person shakes hands with every other person exactly once, how many total handshakes happen?
Stage 3:	If you have FOUR people in a room and each person shakes hands with every other person exactly once, how many total handshakes happen?
Stage 4:	If you have FIVE people in a room and each person shakes hands with every other person exactly once, how many total handshakes happen?
Stage 5:	So, if you have SIX people in a room and each person shakes hands with every other person exactly once, how many total handshakes happen? SEVEN people? EIGHT people?

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