Despite the advance of technology, pencil-and-paper puzzles are still extremely popular, even in mobile apps (which may simulate the behaviour of paper). One such puzzle is the classic “connect-the-dots” puzzle, in which a sequence of dots should be connected to form a picture. Such puzzles are still created manually, as the process is hard to automate: the intrinsic geometric and artistic components call for special attention.

We identify three criteria for a good connect-the-dots puzzle. First, the unsolved puzzle should not reveal the final image (obfuscation). Second, the puzzle should have a unique solution, and no near-solutions (non-ambiguity). Third, the solved puzzle should look like the input image (similarity). We modelled these criteria mathematically, and developed algorithms to optimise them. We implemented these algorithms and generated several puzzles.

Apart from generating classic connect-the-dots puzzles, we also introduce and analyse several new variants. In “Connect-That-Dot” puzzles, the numeric clues are replaced by directional clues. In “Connect-The-Closest-Dot” puzzles, dots should be connected to the nearest dot of the same colour. Finally, in “Connect-The-Unit-Dots” puzzles, dots should be connected only if they are at the correct distance from each other.