Question 80
On a lake there is a village of huts placed on stilts in the nodes of a rectangular grid $m \times n$ (see example in the figure). From the platform of each hut, exactly $p$ bridges start, which connect it to one or more of the adjacent huts (with respect to the grid, therefore not diagonally). For which positive integer values $m, n$ and $p$ is it possible to place bridges $i$ so that from each hut you can reach any other hut? (Obviously more bridges can be placed between two adjacent huts).
