Busy Beaver

on YouTube ↗06m

" summary

Defines the Busy Beaver game: for n states find a Turing machine that writes the maximum number of ones on a blank tape before halting, and shows a live Turing-machine simulator flipping tape cells and changing states so halting vs nonhalting is visible. Notes concrete values: 1→1, 2→4, 3→6, 4→13 and the 5-state value 4,098 proven in 2024. Explains hardness from the halting problem and enormous lower bounds for six states (greater than 10^18,000 using large-number notation).

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