Ana and Bob are playing the following game.
[*] First, Bob draws triangle ABC and a point P inside it.
[*] Then Ana and Bob alternate, starting with Ana, choosing three different permutations σ1, σ2 and σ3 of {A,B,C}.
[*] Finally, Ana draw a triangle V1V2V3.For i=1,2,3, let ψi be the similarity transformation which takes σi(A),σi(B) and σi(C) to Vi,Vi+1 and Xi respectively (here V4=V1) where triangle ΔViVi+1Xi lies on the outside of triangle V1V2V3. Finally, let Qi=ψi(P). Ana wins if triangles Q1Q2Q3 and ABC are similar (in some order of vertices) and Bob wins otherwise. Determine who has the winning strategy. combinatoricsgeometryGame Theory