Consider a table consisting of $2\times 7$ squares. Each little square is surrounded by walls (each internal wall belongs to two squares). We would like to remove some internal walls to make it possible to get from any square to any other one without crossing walls. How many ways can we do this while removing the minimal possible number of internal walls? The figure shows a possible configuration, the remaining walls are marked in red, the removed ones are marked in light pink. Two configurations are considered the same if the same walls are removed.