Sunday, December 09, 2007

Kill the Penguins !

Penguins led by the evil Guin Nep have invaded an iceberg ! There are so many penguins on the iceberg that every inch of the iceberg is covered with penguins.

You have to stop the infestation of penguins! You have 5 rockets, which can be used to bombard the iceberg. The rockets are all identical, and can hit any area of the iceberg. Each rocket will explode and kill all penguins within a radius Z of its landing spot. The yield of the rockets can be adjusted, hence, Z can be set to any value you desire. However, all the rockets must be set to the same yield, otherwise the launching platform will malfunction.

Your task is to choose 5 spots to target the five rockets at. Also, you must choose the minimum yield needed to kill all the penguins. In other words, choose 5 spots and the smallest Z such that the each spot of the iceberg is covered.

The final piece of information needed before you can save the iceberg from the penguins is that the iceberg happens to be in the shape of a perfect circle of radius R.


lightsaber8884 said...

This kinda of remind me of metric spaces and epsilon-nets lol.

Jackson Tan said...

Bah! I decry the murder of these penguins!


In any case, I'm not a mathematician: I shall surround the iceberg with sharks.


The Negative Man said...

I'll need to find some way to remove the sharks after that.

Jackson Tan said...

Build a Chinese restaurant on the iceberg.

The Negative Man said...

Lol ! That is an interesting answer.

lightsaber8884 said...

Not very sure about this one.

I guess the answer should be

Z = R/2*sec(pi/5) and the 5 points are lying on a regular pentagon of sides of length R*tan(pi\5) centered at the centre of the large circle.

The Negative Man said...

You got the same answer as me.

Although, the optimal solution is slightly better. Unfortunately, I can't figure out how to obtain the optimal solution.

You can read more about this here.