Abstract: Methods and apparatus for inferring purity and ploidy from a sample of cells (e.g., a sample comprising cancer and normal cells) are described. Copy number per cell of interest (e.g., cancer cell) is determined by optimizing purity and ploidy for the sample based, at least in part, on relative copy number profile information. One or more likelihood fit scores are determined for each of a plurality of candidate solutions generated by the methods described herein. A solution is selected based, at least in part on the likelihood fit score(s) and the copy number per cancer cell is determined in accordance with the selected solution.