Upside-Down Triangles

To turn a three-story pyramid of coins (with \(1 + 2 + 3 = 6\) coins) upside down, we only need to move 2 coins: moving the bottom left and bottom right coins next to the top coin.

Now, what if there are \(1 + 2 + 3 +\cdots+100=5050\) coins instead? What is the minimum number of coins we have to move in order to turn this huge, 100-story pyramid upside down?


Bonus: Generalize this for a pyramid of \(1+2+3+\cdots+n\) coins.

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