Question 150
There are $n \geq 1$ cities on a horizontal line. Each city is guarded by a pair of stationary elephants, one just to the left and one just to the right of the city, and facing away from it. The $2n$ elephants are of different sizes. If an elephant walks forward, it will knock aside any elephant that it approaches from behind, and in a face-to-face meeting, the smaller elephant will be knocked aside. A moving elephant will keep walking in the same direction until it is knocked aside.
Show that there is a unique city with the property that if any one of the other cities orders its elephants to walk, then that city will not be invaded by an elephant.
Show that there is a unique city with the property that if any one of the other cities orders its elephants to walk, then that city will not be invaded by an elephant.