Only in theory

The days began to fly by, with snow continuing to blanket not just Kawaguchi, but also the Greater Tokyo Area. Meeting at the secret puzzle cafe in Tokyo, Mimoko happily presented her findings to Rodeo.

"What's this?"

"Don't you remember? For your game against Tanabe-kun, I said you could probably draw if you played perfectly, and... I was right. I took on the role of black and played along with Okaa-chan, with things ending in a draw by repetition at move 40. I then ran the game through an analysis engine, and sure enough, things were completely even. Even if the draw had been forgone, no side had any advantage, so a draw would be inevitable, barring no blunders."

"What are the moves?" Okisato asked.

"Starting off with the same moves you played up until Black's move on move 16, the continuation starts with a long castle, then d captures e7, bishop captures e7, rook d1, h5, c3, bishop d6, queen g5, f5, c captures b4, queen e5, queen h4, f4, bishop d2, g5, queen h3, g4, queen h4, d-rook e8, bishop c3, queen captures c3, b captures c3, bishop-"

"Hold on, the queen gets sacked?" Yuusuke gasped.

"Correct, but it's won back as bishop e7 forces the queen to take it, and then the rook takes the queen on e7. With the queen trapped, Black didn't need to rush to capture it."

"You couldn't visualize that all in your head?" Okisato asked.

"I- I could! But Rodeo, poor guy's steamin' out of his ears!"

Sure enough, poor Rodeo was steaming and looking like he was ready to slump to the floor.

"My apologies, Gorou-kun. Though there's only a few more moves until a possible draw. Next is rook e1, rook g7, a-rook d1, bishop e4, f3, rook d3, f captures d2, bishop captures b7, check, king captures b7, king captures g2, rook f8, rook e4, rook f6, e-rook d4, king c6, and then a possible out as rook c4, check, leads to king c6. Then just move the c-rook to d4, the king comes back to c6, and rook c4, check, repeat until threefold."

"Hmm, but White might not choose to repeat," Okisato countered.

"Yes, but like I said, I put the game through an engine afterword. At 37. Rc4+, the eval bar is at +0.3. I'm sure you know what that means, yes?"

"Draw territory."

"Precisely. And if say for move 39, White goes a5, d6, c4, and g-rook f7 later it's dead even on the bar. And if both players know it's even, might as well go for the threefold as early as you can."

"Is Gorou-san capable of pulling all that off? He looked lost after move 20. Even Shousen-san couldn't keep up, and he's 1900."

"1901. I got it back up a notch following All-Japan," Yuusuke snarled.

"Hmm, well I'll send a copy of the moves to Gorou-kun for him to view at his leisure then. No need to stress about them now."

...

The days quickly flew by with Christmas Eve and a subsequent party now only a day away. Yet the Troitsky problem was still nowhere close to being solved.

"The big party at Ryokoma is tomorrow night. That means tonight and next morning are all I have left if I want to try and solve this as a Christmas gift to Inoue-senpai. Alright, let's see if the AI can get it if I feed it everything we know about this game," Okisato thought as he sat in his room.

The response was different from before, but not in the way Okisato would have liked it to be.

"Troitsky-Vogt... My calculations suggest the position in this game could only have been achieved via illegal moves."

"No, it is a real game," Okisato countered.

"Unfortunately, that doesn't seem to be the case. This position cannot be achieved through normal play. It must have been specifically crafted for an end game composition."

It was a back-of-the-mind-fear Okisato had ever since he first began exploring this; what if the Troitsky-Vogt game was nothing but an endgame puzzle and not a real game?"

"No, I refuse to accept this! Inoue-senpai is confident this is a real game, and even if it was crafted specifically for a endgame puzzle, there must be a sequence of moves leading up to it to show it's possible. Otherwise, what's the point of making it if it's not theoretically possible!?"

Thoughts then began flowing into Okisato's head. The double stalemate, Mimoko proving her theory in regards to his game with Rodeo.

"Damn the AI, I'll figure this out myself!"

But that was easier said than done. Still a tad influenced by the AI, Okisato first attempted to solve the puzzle by first playing out all the moves the AI had suggested up until they became impossible to make. From there, he then tried to figure out how to get the final position, but to no avail.

"Nothing. The Sicilian seems like the normal way for things to open- WAIT, no! Black's c-pawn never moves! Arg, dammit! I'll start with e4 and e5!"

Okisato tried, but no matter what, he just couldn't get the position.

"I get it was 1896, but just what did these two play to get that position? It's far too irregular... Irregular..."

With one final hope still in the air, Okisato reset the board.

The full game:

White: Maestro Himitsu (Daria Inoue) Black: Mimoko Inoue

1. Nc3 c5

2. e4 a6

3. d4 cxd4

4. Qxd4 Nc6

5. Qe3 b5

6. a4 Qa5

7. Nf3 e6

8. Bd3 Nge7

9. Nd2 b4

10. Nc4 Qc7

11. Nd5 exd5

12. exd5 Na5

13. Nxa5 Qxa5

14. d6 Bb7

15. O-O Qd5

16. Qg3 O-O-O

17. dxe7 Bxe7

18. Rd1 h5

19. c3 Bd6

20. Qg5 f5

21. cxb4 Qe5

22. Qh4 f4

23. Bd2 g5

24. Qh3 g4

25. Qh4 Rde8

26. Bc3 Qxc3

27. bxc3 Be7

28. Qxe7 Rxe7

29. Re1 Rg7

30. Rad1 h4

31. Be4 f3

32. Rd3 fxg2

33. Bxb7+ Kxb7

34. Kxg2 Rf8

35. Re4 Rf6

36. Red4 Kc6

37. Rc4+ Kb6

38. Rcd4 Kc6

39. Rc4+ Kb6

40. Rcd4 Kc6