ClearAll[PermuteState]
PermuteState[state_, {rc_, n_Integer}] := Module[{s},
  s = state;
  Switch[rc, "R",
   s[[n]] = 1 - s[[n]],
   "C",
   s[[All, n]] = 1 - s[[All, n]]
   ];
  s
  ]
SeedRandom[1337];
n = 3;
goalstate = state = RandomChoice[{0, 1}, {n, n}];
While[goalstate == state,
  permutations = {RandomChoice[{"C", "R"}, 20], RandomInteger[{1, n}, 20]} // Transpose;
  state = Fold[PermuteState, state, permutations];
];
i = 0;
history = {state};
Grid[goalstate, ItemSize -> {5, 3}, Frame -> True]
b1 = Button["", state = PermuteState[state, {"C", #}];
     AppendTo[history, state]; i++;
     If[state === goalstate, MessageDialog["You Won!"];
      Print[Grid[#, Frame -> True]] & /@ history]] & /@ Range[n];
b2 = Button["", state = PermuteState[state, {"R", #}];
     AppendTo[history, state]; i++;
     If[state === goalstate, MessageDialog["You Won!"];
      Print[Grid[#, Frame -> True]] & /@ history]] & /@ Range[n];
Dynamic[Grid[
  Prepend[MapThread[Prepend, {state, b2}],
   Prepend[b1, Row[{"Flips: ", i}]]], Frame -> True
]]