In one of his numerous conferences, Frank Harary, talked about one of his many games, that, as usual, had a very difficult problem associated to it. In this case, a family of games for two players in which the selected number of columns in the game has a vital importance. He has proved that for 2 and 3 columns the longest match has 9 and 24 moves respectively, that is to say that h₂=9 and h₃=24. At the same time it was announced that he knew a solution of length 67 for the problem with 4 columns, but he didn't know if it was the maximum. We present here a program that proves that h₄=67. Although it uses but a brute-force approach, its soundness seems good fun to prove.