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Parsons problems, originally called Parson’s Programming Puzzles, are drag-and-drop computer programming problems that require learners to place code blocks in the correct order and indentation. Introductory computer programming instructors use Parsons problems to engage novice programmers in actively learning how to code while optimizing problem-solving efficiency and cognitive load. But while there has been a great deal of research on the design of active learning techniques such as Parsons problems and block-based programming for neurotypical individuals—people without disabilities—and programmers with visual or motor impairments, learners with cognitive disabilities have received relatively little attention. Are Parsons problems accessible to novice programmers with cognitive, learning, and neurological disabilities? In this paper, I report on the findings from an exploratory multiple-case study with neurodiverse programmers to highlight the accessibility barriers and benefits they experienced while learning how to program by solving Parsons problems at the end of eight chapters from an interactive eBook on Python. Within-case analyses of 15 think-aloud observations with five novice programmers led to the generation of four working hypotheses about improving the cognitive accessibility of Parsons problems for programmers with and without disabilities. And finally, a cross-case analysis showed similarities in participants’ average interaction with Parsons problems, the mental effort they invested in solving them, and participants’ beliefs about and strategies for problem-solving. These findings have implications for personalizing Parsons problems and developing support features for neurodiverse programmers.