## Wednesday, August 10, 2016

### you have 90 seconds

It took me about a minute and a half to solve this problem, which I saw on YouTube:

In the comments, leave your answer in terms of pi, or use a calculator to give an answer in 4 decimal places (please round).

For confirmation, go watch the video, which offers two solutions: a simple solution involving commonsense geometry, and an unnecessarily complex solution involving higher math.* One of the commenters to the video notes that even sixth-grade Chinese kids might have trouble solving this. Since I used to tutor this stuff, though, I found it easy. Every once in a while, it's good to flex the brain muscles by doing little math problems like this.

(My handwritten solution is here.)

*CORRECTION: the video actually goes on to consider a substantially more complicated problem: how to calculate the irregularly shaped area of one corner of the figure. That's a different animal altogether, and that's what I get for watching the video in my office with the audio off! Serves me right.

1. Took me less than a minute because I immediately saw the shortcut:

The simplification (which allows you to dispense with paper and pencil) is to notice that if you twist the diagonal to the vertical, the answer pops out as:

The area of one of the squares minus the area of one of the circles.

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