Can I use the Excel File that I download from this website to play the Busy Beaver Game?

Yes, you can!!

At first, I was going to answer "No, you can't!" because a Busy Beaver Turing Machine must start with a completely blank tape. But the Penrose type of Turing Machine that you can download from this website must have at least one 1 on the tape, or else it will just run forever looking for the first 1, because in the Penrose Turing Machine, the first instruction (when state is 0 and tape reads 0) must always be 00R.

However, there is a way to do it.

---

Just make sure that the data on the tape is just one 1 and nothing else. Then, also make sure that the instruction at state 0 when tape is 1 is 10R. Then, for the rest of the states, just put in the instructions for your Busy Beaver Turing Machine, but none of those instructions should take you back to state 0.

For example, suppose you want to build a Busy Beaver Turing Machine with 3 states. Then, state 0 should be constructed as explained above; it is not part of the Busy Beaver. The next 3 states (labeled 1, 10, and 11 in binary) are the Busy Beaver states. So, in total, you really have 4 states (labeled 0, 1, 10, and 11) but only the last 3 make up the Busy Beaver Turing Machine.

When you start running your Turing Machine that you just built this way, the first step that it will take will just be to clear the single 1 that you put on the tape. That first step does not count toward the the number of steps taken by the Busy Beaver; but the rest do.

---

A good Busy Beaver Turing Machine with 3 states is the one whose Turing Machine Number is 10861728875894229.

Why don't you go ahead and try it!

When you do try it, you'll see that when this Turing Machine stops, there will be six 1's on the tape. Also, the Turing Machine will stop on the 15th step. However, step #1 was not part of the Busy Beaver part of this Turing Machine, so it doesn't count, so the Busy Beaver took 14 steps before it stopped. By the way, that is the best that any 3-state Busy Beaver can do.