I solved (believe) the puzzle in 3 minutes. A says B result is the same as A result. B says A result is different from B result, so that A covers (H,H) and (T

I solved (believe) the puzzle in 3 minutes. A says B result is the same as A result. B says A result is different from B result, so that A covers (H,H) and (T,T), B covers (H,T) and (T, H), so always A or B is true, so they always win.