[borisp]

This is twice now that I've posted problems with the expectation to stump the forum...only to be "disappointed" with a clever answer in under twenty minutes [img]/images/graemlins/smile.gif[/img]

busto, I challenge you to solve the other one...suppose that each cell in an nxn grid of cells is marked either "infected" or "healthy," and that a healthy cell becomes infected if it shares at least two edges with infected cells. Further assume that the process of infection continues until it stabilizes.

Show that for the entire grid to be infected at the end, it must have been true that at least n cells were infected to begin with.