BB(3,6)

The 3-state 6-symbol Busy Beaver problem, BB(3,6), is unsolved and unexplored. With Cryptids like Hydra in the preceding domain BB(2,5), we know that we must solve a Collatz-like problem in order to solve BB(3,6). The current BB(3,6) champion is 1RB3LB4LC2RA4LB5LB_2LC3RB1LC2RA5LC1RZ_3RB1LB3LC2RC4LC5LC (bbch), it was constructed by Loader3229 and runs for more than $f_{\omega }^3(15)$ steps.

BB(3,6) is expected to be very hard to enumerate.