A lion and a lion tamer are enclosed within a circular cage. If they move at the same speed but are both restricted by the cage, can the lion catch the lion tamer? (Represent the cage by a circle, and the lion and lion tamer as two point masses within it.)

If the tamer insists on running in a predictable way around the circle the lion can plot an intercept course rather than heading straight for the tamer.  For example the the lion and tamer were both at the edge of the cage with a separation of 90(1-2√2/π)≈8.97 degrees the lion could head straight for a point exactly 1/4 of the way around.

The slight problem here is that the lion will, for a time, increase his distance from the tamer.  This means an intelligent tamer could double back and the lion would be forced to respond.

The lion could use this idea to trap the tamer within a portion of the cage.  Unfortunately the time required to shrink the portion to zero with a zig-zagging tamer is infinite.

Posted by Jer on 2013-06-11 14:22:02