This paper discusses the theoretical problem 3 of the 54th International Physics Olympiad (IPhO). The title of the problem is called Black Widow Pulsar. At glance it appears similar to the APho (Asia Physics Olympiad) 2024 theoretical problem 3, however the essence is a typical mechanics problem about the accretion of binary star system and the equilibrium of a single gas star. The question is composed of two parts, first is concerned with the transfer of mass (accretion) in a binary star system; the second is the equilibrium of a single gaseous star, under the influence of gas pressure and gravity. It utilizes classical models in mechanics and decent in difficulty and quite suitable for high school Olympiad students. This is common feature for this 54th IPhO. A detailed description and answer to this problem is given here.