Statistics-based colour constancy algorithms work well as long as there are many colours in a scene, they fail however when the encountering scenes comprise few surfaces. In contrast, physics-based algorithms, based on an understanding of physical processes such as highlights and interreflections, are theoretically able to solve for colour constancy even when there are as few as two surfaces in a scene. Unfortunately, physics-based theories rarely work outside the lab. In this paper we show that a combination of physical and statistical knowledge leads to a surprisingly simple and powerful colour constancy algorithm, one that also works well for images of natural scenes. From a physical standpoint we observe that given the dichromatic model of image formation the colour signals coming from a single uniformly-coloured surface are mapped to a line in chromaticity space. One component of the line is defined by the colour of the illuminant (i.e. specular highlights) and the other is due to its matte, or Lambertian, reflectance. We then make the statistical observation that the chromaticities of common light sources all follow closely the Planckian locus of black-body radiators. It follows that by intersecting the dichromatic line with the Planckian locus we can estimate the chromaticity of the illumination. We can solve for colour constancy even when there is a single surface in the scene. When there are many surfaces in a scene the individual estimates from each surface are averaged together to improve accuracy. In a set of experiments on real images we show our approach delivers very good colour constancy. Moreover, performance is significantly better than previous dichromatic algorithms.