Humans seem to be inherently driven to engage in wordplay. An example is the creation of palindromes – sentences that read the same backward and forward. This activity can be framed as a curiosity-driven behaviour, in which individuals seek for information that serves no direct purpose and in the absence of external rewards. In this fMRI case study, an experienced palindrome creator was scanned while he generated palindromes with different levels of difficulty. Palindrome creation was alternated with resting periods and with a working memory task, both serving as control conditions. Relative to resting, palindrome creation recruited frontal domain-specific language networks and fronto-parietal domain-general networks. The comparison with the working memory task evidenced partial overlap with the multiple-demand cortex, which participates in solving a variety of cognitively challenging tasks. Intriguingly, greater difficulty during palindrome creation differentially activated the right frontopolar cortex (BA 10), a region that was also linked to palindrome resolution. The latter is consistent with exploratory behaviour – in this case, with seeking new but interdependent linguistic segments within a complex internal model (i.e., a palindromic structure)– and bears resemblance with brain substrates sustaining hard logical reasoning, altogether pointing to a commonplace for curiosity in discovering new and complex relations.