The game apparatus has a plurality of elongate coloured building blocks. During the course of a game a number of the blocks are built up block by block in a desired orientation on an associated plinth forming an upright structure until this structure collapses. Each building block is of square section and is subdivided into five coloured engagement portions each of which has a different colour. When building up the structure the coloured building blocks may only interengage where their touching engagement portions are of the same colour.