... and why!

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·Nov 10, 2024

The reason this trick works every single time is elegantly simple. It has everything to do with the fact that their chosen card will always be in a pack that is third from the top.

That's because we had them take the pack containing their card, see? There's Boron, and put it on one of the piles. Then we had them put two more piles on top of that one.

So this stack is in order: pack number one, pack number two, pack number three, which contains their card, and at the bottom, pack number four. When they deal the cards out into rows, they are changing the packs into layers.

See, here we go! We've got 1, 2, 3, four cards. These are the cards that made up pack number one. Here comes pack number two; it is now becoming the second layer.

The third layer will be the components of pack number three, including Boron, their card. So when they finish and take the pack containing their card, because it is part of the third layer, it will be the third from the top, which means it will always be the third card from the left. Boron. [Music]

Finding increasing interval given the derivative | AP Calculus AB | Khan Academy

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