Solved On TV In Only 10 Seconds! Trick To Count Rectangles Quickly

Can you count the number of rectangles in the grid? How about in the L-shaped grid? These problems appeared on the TV show Superhuman hosted by Kal Penn (Kalpen Modi). The contestant Summer gave the correct answer to each challenge in about 10 seconds. It would seem you have to be a savant to count the possibilities so quickly. But in fact anyone can solve the problems with the “super power” of mathematics. In this video I explain a mathematical method for counting rectangles.

By request, here is a version of the video at 88 percent opacity (slightly grey text, like YouTube’s dark theme), but I do not think it looks as nice:

My blog post for this video:

Superhuman TV Show Rectangled Challenge (contains spoiler of the answer–avoid watching if you want to solve it first!)

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