In the Busy Beaver game we ask: what is the longest that a Turing machine program of N states and K colors can run before halting when started on the blank tape? Answering this question requires enumerating every such program and checking whether or not it halts. But there is a big problem: there are just too many to check. The number of programs grows multiple-exponentially with N and K, O(nknk). Yikes!
