Tuesday, February 14, 2006

Answer to the puzzle and the next one

Ario explained it correctly.

Puzzle #2:
Divide a circle into 12 congruent pieces, with equal size and same shape, such that all pieces never meet. It's ok for pieces to be next to each other. But all of them cannot meet at the same point. So you cannot cut the circle in 12 pizza slices as they all meet at the center. This is more visual. Have fun. I first tried doing this with paper. But I was able to get it very quickly after deciding to close my eyes.

BTW, we have posted a very small collection of tech talks given here at Google on, you guessed it, Google Video.


Blogger ario said...

i'll have to read this new one soon... but in the meantime, this page is an interesting resource regarding the coffee/cream problem.

the "elegant" solutions hadn't occured to me, but after reading them, I definitely had a "doh!" moment :)

1:34 AM  
Anonymous Anonymous said...

This liked this one.

The way I solved it (I think) is to first divide the circle into 6 parts using arches that have the same radius as the circle.

- Basically pick a point on the circle
- With this point as the center draw an arc that cuts the circle
- Now choose the point where the previous arc cut the circle as the center and draw another arc and so on

At the end of it you will have 6 symetric pieces that meet at the center of the original circle (Why 6 I'll explain later).

The great thing about these 6 pieces is that each of their sides is an arc of length 2*pi*R/6. SO rather than divide each piece into two by starting from the center you can infact start from one of the outer points drawing astraight line down the center of each segment.

Why 6?

If you connect the center to the two points of each segment the distance between each point is R. Therefore you will get a equilateral triangle whose inside angle must be 60 degrees. The number of such segmenst is therefore 360/60 = 6.

8:59 AM  
Anonymous Anonymous said...

I made a diagram of the solution for the visual-minded out there.

1:26 PM  
Anonymous Anonymous said...

yes it s true!

4:00 PM  
Anonymous Anonymous said...

i couldn t get the answer!

9:59 AM  
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6:02 AM  

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