Reverse Puzzling 7: I FED the CIRcus some DAM GAS

Question

[Continued thematically from here (maybe - in all the excitement, I kinda lost count of it myself)]

I handed George the very famous puzzle and asked him if he knew how to solve it.

"Oh, yes, of course. You insult me. I even have a mnemonic of sorts."

He explained the co-ordinate system that used vowels going down and consonants going across and a couple of the specific moves (like M was "move together" and S was "side-step"). Then he said in a sing song voice as he solved the puzzled:

"I FED the CIRcus some DAM GAS *rotate*
CIRcus DAM GAS *rotate*
CIRcus DAM GAS *rotate*
CIRcus DAM GAS"

"What happens to the co-ordinates when you rotate?" I asked

"Oh, they stay in the same place, so they refer to different parts of the puzzle. Anyway, don't interrupt. I'm almost done now. So, now you *singing again* GO all the way around using FODder from your HOLdall."

"But it's not finished," I pointed out.

"Oh, but it's easy from here. Just FIM and you're done!"

"Very good. That's very easy to remember. Did you invent the mnemonic?"

"No, it's a standard notation invented by David whatzizname. I just applied it to my favorite solution."

What puzzle did I give George, and what solution did he remember with the mnemonic? And what is David's name?

Answer 1

[Note: when this answer was written there was a minor error in the puzzle, which had BIRds rather than CIRcus. The puzzle has been fixed but I haven't updated the answer.]

The puzzle is

peg solitaire (with 33 holes and 32 pegs)

and David's surname is

Wolstenholme.

The notation

labels the rows of the board AEIOUWY from top to bottom, and the columns BCDFGHJ from left to right. A single move jumping over one peg is specified by giving the column and then the row of the peg that jumps, followed by the direction (one of R,L,U,D). The direction can be omitted when only one move is possible for the selected peg. There are separate notations for some common sets of moves, which you can find at this webpage but as of 2021-08-31 the server had an out-of-date certificate, so your browser may complain if you try to go there.

So, we start with

  B C D F G H J
A     o o o
E     o o o
I o o o o o o o
O o o o . o o o
U o o o o o o o
W     o o o
Y     o o o

and FED the BIRds some DAM GAS

by jumping FE down, BI right ... except that that's impossible, and we actually do it with CI ..., and then doing a "meet-in-the-middle" starting at DA, which means we jump that peg one way and then another over it in the opposite direction, turning something that looks like o o . o into . o . ., and then doing a "side-step" starting at GA, which means we jump that peg twice at a 90-degree angle, in this case left and then down. That gives us this:

  B C D F G H J
A     . . .
E     . . o
I o . o o o o o
O o o . o o o o
U o o o o o o o
W     o o o
Y     o o o

Now we

rotate the board 90 degrees clockwise, and do the BIR DAM GAS steps again; do that again; and do it again. At this point we have rotated three times and done four lots of BIR DAM GAS, and what remains is:

  B C D F G H J
A     . . .
E     . o .
I . . o o o . .
O . . . o o o .
U . . o o o . .
W     . o .
Y     . . .

Now we

"GO all the way around", meaning to take the GO peg and jump it six times; it does indeed "go all the way around", and ends up back where it started, and whichever direction we do the jumping in the result is the same:

  B C D F G H J
A     . . .
E     . . .
I . . . o . . .
O . . . o o o .
U . . . o . . .
W     . . .
Y     . . .

And now

after doing a FOD and a HOL, we have three pegs in a vertical o o . o configuration and a final FIM removes the outer two, leaving us with a single peg standing triumphantly in the centre of the board.

  B C D F G H J
A     . . .
E     . . .
I . . . . . . .
O . . . o . . .
U . . . . . . .
W     . . .
Y     . . .