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Holiday Tree Puzzle

My student Amanda reminded me of the classic triangle puzzle (n=1), so I thought about making a pattern of puzzles. The puzzle is to fill each side of the triangle in with one each of the numbers 2, 3, 4 ... (as high as you need), and then the last number in the star. Is there a pattern to the numbers that go in the star? How high will the tree be at each step? Is there a pattern to how you solve the puzzles? Is there a pattern to the common sum that the sides have? Yes, Virginia, there are all these patterns! Math is the gift that keeps giving.