What-Comes-Next (WCN) puzzles require the candidate to identify the next figure that ``logically follows" a sequence of figures shown to them. WCN puzzles are a favorite of interviewers and examiners—there is hardly any aptitude test that misses WCN puzzles. In this work, we propose to automatically synthesize WCN puzzles. The key insight to our methodology is that generation of WCN problems can be posed as a program synthesis problem.
We design a small yet expressive language, $PuzzleLang$, to capture solutions to WCN puzzles. $PuzzleLang$ is expressive enough to explain almost all human generated WCN puzzles that we collected, and yet, small enough to allow synthesis in a reasonable time. To ensure that the generated puzzles are appealing to humans, we infer a machine learning model to approximate the $appeal-factor$ of given WCN puzzle to humans. We use this model within our puzzle synthesizer as an optimization function to generate $highly-appealing$ correct-by-construction WCN puzzles.
We found that $PuzzleGen$ is fast, clocking an average time of about 3.4s per puzzle. Further, statistical tests over the responses from a user-study supported that the $PuzzleGen$ generated puzzles were indistinguishable from human created puzzles.
