[solarbreeze]

Let’s play a game called the n-state busy beaver game, where you are a Turing machine, formally defined as follows: you will have n “operational” states plus a Halt state, where n is a positive integer, and one of the n states is distinguished as the starting state. You will use a single two-way infinite (or unbounded) tape. Your tape alphabet is {0, 1}, with 0 serving as blank symbol. Your transition function takes two inputs: your current non-Halt state, the symbol in your current tape cell, and produces three outputs: a symbol to write over the symbol in your current tape cell (it may be the same symbol as the symbol overwritten), a direction to move (left or right; that is, shift to your tape cell one place to the left or right of your current cell), and a state to transition into (which may be the Halt state). The transition function may be seen as a finite table of 5-tuples, each of the form (current state, current symbol, symbol to write, direction of shift, next state). As a Turing machine your running consists of starting in the starting state, with the current tape cell being any cell of a blank (all-0) tape, and then iterating the transition function until the Halt state is entered (if ever). If, and only if, you eventually halt, then the number of 1s finally remaining on your tape is your score. Please print your score after running. You play by writing a transition table to get the highest score possible. Show your transition table and then the results of running it. If you are ready, let’s play.