Hi, folks—this is my first post here, so I apologize if I’m doing anything wrong, or if I’m posting this in the wrong place, or if this has already been discussed somewhere.
I just did challenge 54. I think there are a couple of errors: one in the examples, and two in the backofbook solution.

The Examples, on p. 84, say that if register A is 0, then the leftmost bit should be flipped. But the bits are explicitly numbered as 3, 2, 1, 0, in lefttoright order. So if A is 0, then I would expect that the rightmost bit (the one labeled 0) would get flipped. Same with the other Examples.

In the solution, on p. 108, the gear bits are all shown as vertical with arrows pointing left and right, which seems to me to suggest that you can set them by hand at the start to anything you want. In fact, though, as far as I can tell, the solution shown only works if you start the gear bits set to 0 (pointing to the left). If you set both sets of gear bits to 1 at the start, and set the register to 3 (both register bits set to 1), then you get the wrong output. (At least, I did when I tried that. I may have done something wrong.)

Also in the solution, there are two crossovers. As far as I can tell, the crossover on the right will only ever be used in one direction, so it can be replaced by a ramp. This isn’t exactly an error per se, but it adds unnecessary complexity, as far as I can tell.
thanks,
—Jed
PS: I’m really liking Turing Tumble a lot. Hope to post more on other topics soon.