  Throughout history, recreational mathematics has always played a prominent
role in advancing research. Following in this tradition, in this paper we
extend some recent work with crazy sequential representations of numbers-
equations made of sequences of one through nine (or nine through one) that
evaluate to a number. All previous work on this type of puzzle has focused only
on base ten numbers and whether a solution existed. We generalize this concept
and examine how this extends to arbitrary bases, the ranges of possible
numbers, the combinatorial challenge of finding the numbers, efficient
algorithms, and some interesting patterns across any base. For the analysis, we
focus on bases three through ten. Further, we outline several interesting
mathematical and algorithmic complexity problems related to this area that have
yet to be considered.
