German Version

Take a 1x1 square. Count how many squares there are total (duh). Now take a 2x2 square. Count the total number of squares (including the larger one that is formed by the outside of the whole thing). Take a 3x3 square and find the total. How many squares would there be in a 10x10 square? How about an NxN square?

Now do the same thing with triangles - take a look at the pictures below. How many total triangles in a triangle that's 10 units on a side? How about N units?

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