Puzzle #11 – Terra Fermat

I recently watched The Hunger Games: Catching Fire. By means of a convenient plot device, Katniss ends up back in the arena. She is immediately presented with a test of her physical intuition.


In the centre of the arena is a circular lake. The lake is divided into twelve circular sectors of equal size by rocky pathways. The pathways converge on an island bearing the cornucopia, housing a bounty of weaponry.

The twenty-four tributes start in one of the circular sectors on a small pedestal, some distance from the cornucopia.

Suppose Katniss can swim at speed u and run at speed v. For simplicity we’ll assume both u and v are constant. Assume also that v>u.


Question: At what angle should Katniss approach the nearest rocky pathway such that she reaches the cornucopia in the least possible time?

Hint: It is easiest to define the angle as being that which Katniss’ path subtends with the normal to the pathway.


One thought on “Puzzle #11 – Terra Fermat

  1. Pingback: Terra Fermat Solution | Conversation of Momentum

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s