You have a perfectly cylindrical glass completely full of water (no rounded edges on the bottom, same diameter all the way down). How do you empty out exactly half of the water? There are no markings on the glass and you have nothing else to work with.

Solution:

Tilt the glass until the surface of the water reaches from the top edge on one side of the glass to the corner of the bottom on the other side, about 45-60 degrees, depending on the size of the glass. That way the glass will be half full of water, half full of air.

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Slowly tip it sideways, spilling, until the level of the water reaches the bottom corner of the glass.

ReplyDeleteBonus question: how do you empty exactly one third?

What?! You are outquestioning me. I will have to think about that

ReplyDeleteWait, is that even possible? This is like trisecting an angle with a compass, isn't it?

ReplyDeleteStrong, is there actually an answer to the 1/3 variation?? Seems impossible; don't know if you're just screwing with us...

ReplyDeleteMy layman's guess is: shake the glass in a little orbit on the table, so as to set up a whirlpool. Water spills out the sides. Keep shaking until the speed of the whirlpool is such that the bottom of it reaches the bottom of the glass. That being accomplished, a cone of water will have spilled out; and the cone has a volume 1/3 the glass'.

ReplyDeleteA pointy cone? The whirpool has the shape of a parabola (centripetal force proportional to the square of the radius), which actually takes up half the volume.

ReplyDelete