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This is an archived problem from a previous year. Submissions are closed, but you can view the problem and its solution.

19

ditto chess

As the last pawn is placed and the correct move played, the entrance to Santa's Workshop unlocks with a chorus of mechanical clicks.

Inside Santa's Workshop, you and the group start gathering chess gear. You suddenly see a wooden chessboard, strikingly similar to the one from the North Pole pub.

"Hold on," you say, picking up the board. "Did anyone here play against an elf at the pub who mirrors every move?"

The elves exchange puzzled looks. David Snowell shakes his head, "I don't think any of us have seen that at the pub. Mirror chess isn't a common strategy around here."

You turn to Wesley Snow, "You saw the elf I played against, right?" Wesley's answer surprises you. "When I approached you, you were alone, analyzing a chess position."

Confused, you insist, "But I was playing a game... with someone."

Magnus Carolsen joins in on the conversation, "Sometimes our minds play tricks on us."

As you study the chessboard more closely, you notice the position seems reminiscent of a mirrored game. "It looks like this position was reached through a mirror game, just like the one I played against that elf at the pub," you say.

The elves gather around, looking skeptical. "Are you sure?" David asks, examining the board.

"The board says 'Ditto Chess', sounds like both sides must copy one another!", you say. Still not convinced, David asks you to demonstrate how this position can be reached under these weird conditions.

In Ditto Chess, whenever the side to play can legally copy the other side's previous move, they must do so (if they can't, they may play any legal move). As always, a move is not legal if it leaves your king in check*.

A move is only a copy of another move, if:

1) the type of piece that's used is the same

2) the copying move starts and ends on the horizontally mirrored squares of the original move (e.g. Qa1-b2 is a copy of Qa8-b7)

3) the moves both capture the same type of piece (or both capture no piece at all)

* For simplicity, these rules are incomplete. All rules needed to solve the problem are included. Ditto Chess is a fairy condition invented by Joachim Hambros.

Given these rules, give a sequence of moves that starts from the initial position and reaches this position in exactly 6 moves (6 moves for White and 6 moves for Black).

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