But for how long? Let's take it from the top!
Be ready to allocate upwards of 16.7KB of memory for this task, you eager beavers you.
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It is hinted
from the words "busy" and "beaver" that the image is a depiction of a Turing machine (a busy beaver is a halting 2-symbol Turing machine printing the most ones). The markings on the ends of the edges denote various aspects of the transition (no flipping!)
Number the states 0 to 5 starting from the top and going clockwise. The transitions are given below in (old state, old symbol, new symbol, movement direction, new state) format:
We start at state 0 ("take it from the top").
when implemented in C++ the above Turing machine halts after 13,122,572,796 steps, which is how long they'll be kept busy for. 204,918 positions are used, of which 136,610 are ones.