Humans seem to be inherently driven to engage in wordplay. An example is the creation of palindromes –words, sentences, or even paragraphs that read the same backward and forward. This type of activity can be framed as a curiosity-driven behavior, in which individuals sacrifice finite resources, such as their time, to seek information that serves no direct purpose and in the absence of external rewards. Here, we present a single-case fMRI study of an experienced palindrome creator, who was scanned while he was immersed in generating palindromic sentences with different levels of difficulty. Blocks of palindrome creation were alternated with periods of resting and with the performance of a simple working memory (WM) task that served as control conditions. Relative to resting, palindrome creation recruited frontal domain-specific language networks and fronto-parietal domain-general networks. The comparison with the WM task evidenced a partial overlap with the multiple-demand cortex (MDC), which participates in solving different cognitively challenging tasks that require attention and cognitive control. Further, the implication of the inferior temporal gyrus (BA 37), extending ventrally to occipito-temporal regions (including the visual word form area), suggested the use of visual imagery and word form visualization to achieve this challenging task. Notably, greater difficulty during palindrome creation (difficult minus easy blocks) differentially activated the right frontopolar cortex (BA 10), a region that was also linked to successful palindrome resolution. The latter is in line with exploratory behavior to seek out information, in this case, with the exploration of new but interdependent linguistic segments within a complex internal model (i.e., a palindromic structure). These brain substrates also bear resemblance with those sustaining hard logical reasoning, altogether interestingly pointing to a commonplace for curiosity in discovering new and complex relations.