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Triangle Numbers

20 people at a party gives gifts to each other. How many gifts were given? 20 people at a party shake each others hands. How many handshakes were there? An ice cream store has 20 flavors. How many different ways can you pick 2 different flavors? When Gauss was very young he found a fast way to add up all the numbers from 1 to 100. Can you? What is the nth triangle number?