Block-based visual programming environments play a critical role in introducing computing concepts to K-12 students. One of the key pedagogical challenges in these environments is in designing new practice tasks for a student that match a desired level of difficulty and exercise specific programming concepts. In this paper, we formalize the problem of synthesizing visual programming tasks. In particular, given a reference visual task $rm T^{in}$ and its solution code $rm C^{in}$, we propose a novel methodology to automatically generate a set ${(rm T^{out}, rm C^{out})}$ of new tasks along with solution codes such that tasks $rm T^{in}$ and $rm T^{out}$ are conceptually similar but visually dissimilar. Our methodology is based on the realization that the mapping from the space of visual tasks to their solution codes is highly discontinuous; hence, directly mutating reference task $rm T^{in}$ to generate new tasks is futile. Our task synthesis algorithm operates by first mutating code $rm C^{in}$ to obtain a set of codes ${rm C^{out}}$. Then, the algorithm performs symbolic execution over a code $rm C^{out}$ to obtain a visual task $rm T^{out}$; this step uses the Monte Carlo Tree Search (MCTS) procedure to guide the search in the symbolic tree. We demonstrate the effectiveness of our algorithm through an extensive empirical evaluation and user study on reference tasks taken from the emph{Hour of Code: Classic Maze} challenge by emph{Code.org} and the emph{Intro to Programming with Karel} course by emph{CodeHS.com}.
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