An open question in mathematics that has yet to be resolved is as follows: given an $N\times N$ boggle grid, how many total simple (non-intersecting, in the sense of not returning to the same node twice) paths, including paths of length zero, are there?
Despite the seemingly simple nature of this question, the answers are only known up to $N=5$, and they are as follows:
$$1,64,10305,12029640,115066382913$$
Does anyone have any additional insight on this problem?