Alice and Bob are playing hide and seek. Initially, Bob chooses a secret fixed point B in the unit square. Then Alice chooses a sequence of points P0,P1,…,PN in the plane. After choosing Pk (but before choosing Pk+1) for k≥1, Bob tells "warmer'' if Pk is closer to B than Pk−1, otherwise he says "colder''. After Alice has chosen PN and heard Bob's answer, Alice chooses a final point A. Alice wins if the distance AB is at most 20201, otherwise Bob wins. Show that if N=18, Alice cannot guarantee a win. combinatoricscombinatorics proposed