Title: Self-Supervision is All You Need for Solving Rubik's Cube. Abstract: While combinatorial problems are of great academic and practical importance, previous approaches like explicit heuristics and reinforcement learning have been complex and costly. To address this, we developed a simple and robust method to train a Deep Neural Network (DNN) through self-supervised learning for solving a goal-predefined combinatorial problem. Assuming that more optimal moves occur more frequently as a path of random moves connecting two problem states, the DNN can approximate an optimal solver by learning to predict the last move of a random scramble based on the problem state. Tested on 1,000 scrambled Rubik's Cube instances, a Transformer-based model could solve all of them near-optimally using a breadth-first search;  with a maximum breadth of $10^3$, the mean solution length was $20.5$ moves. The proposed method may apply to other goal-predefined combinatorial problems, though it has a few constraints.