Hmm.<!-- let the square be ABCD and the grasshopper be at A initially.
let G1={A,C} and G2={B,D}. The grasshopper's position must alternate between G1 and G2, so.. it could only be at A (in G1) after a even number of jumps.. and 9 is not even. so it must be at B or D after 9 moves.
after 1...