MathDB

On a board with

a

rows and

b

columns, each square has a switch and an unlit light bulb. By pressing the switch of a house, the lamp in that house changes state, along with the lamps in the same row and those in the same column (those that are on go out and the that are off light up). For what values of

a

and

b

is it possible to have just one lamp on, by pressing a series of switches?

Problem Statement