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Removed 5D chess

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Mark 2024-05-24 16:24:27 -07:00
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21
Advanced/5D Chess/main.tex
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\documentclass[
solutions,
shortwarning
]{../../resources/ormc_handout}
\usepackage{../../resources/macros}
\uptitlel{Advanced 2}
\uptitler{\smallurl{}}
\title{5D Chess}
\subtitle{
Prepared by Mark on \today{} \\
Based on \href{https://steamcommunity.com/sharedfiles/filedetails/?id=2177978276}{\texttt{[this]}}
Steam post.
}
\begin{document}
\maketitle
\input{parts/01 rook}
\end{document}

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Advanced/5D Chess/parts/01 rook.tex
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\section{Rook Tactics}
\problem{Rook Tactics I}
At first it seems like there's no useful moves you can make ---
if you check the King in the present with your Rook, it just
walks out of the way. Moving your King into the present or past
seems to do nothing exciting (you've only got one turn and it
never puts the king in check, so it's a non-starter).
What if we think five dimensionally?
We can try moving the rook into the past - but the king on the new timeline just moves out of check.
What we need to realize is - the Rook can't just MOVE into the past. It can also CAPTURE into the past. Can we use this to our advantage? Can we do a kind of check that is impossible in 2D chess?
Just move your rook to the northeast corner.
It checks the king in the past.
(The AI can't branch to get away from it since it
would advance the checked timeline and allow me to
make my checkmating move, and it has no other timelines
it can branch to recede the Past while choosing to not
play in the checking timeline.)
\problem{Rook Tactics II}
This would be checkmate in typical chess.
But thanks to time travel, our opponent has a trick up their sleeve.
Do the standard (as in Chess) mate. Enemy king will branch to remove
their present king from check (they can do it since it's not threatened
in the past in that timeline, so it removes the check condition).
Then do the same move again in the new branch. Too bad they couldn't run further!
\problem{Rook Tactics III}
In the last puzzle we saw travel into the past.
But there is one more dimension that pieces can move and attack along.
Move a rook fully north to check a king across timelines.
(The AI can't do anything here except move its pawn -
it again has no other timelines available to branch to recede The Present.
We weren't obliged to play on the future timeline, and in fact if we do
the AI can get out of it by sending their king into the past to capture
our rook. So we have to make a move and NOT make another move.)
\problem{Rook Tactics IV}
Rook Tactics IV: Some things we can try that don't work: The black rooks can make moves into the past and across timelines, but don't result in check.
Also doesn't work: We can move the top board black rook to check a present king, but the present king can just move, so this this leads to nothing good.
So instead, what if we move the top board black rook onto the position a white king used to be in? Then it threatens check by moving into the past to capture the past king.
But the white king in the present can capture the black rook.
Therefore the solution is... To move the bottom board black rook into the same rank and file as the bottom board black rook! Then the top board black rook is protected and can't be captured by a king (it would be captured back by the bottom board black rook). This is checkmate.
\problem{Rook Taactics V}
Do the standard Chess mate. Again, enemy king will branch to remove their present king from check.
Now what? We can check the king with the rook in the new branch, but surely it'll just get captured by the king to stop mate, right? Are we meant to do something else instead?
(One last hint: Pieces can be defended from other timelines.)
Nope! Just move the rook to the same position. Well, why does it work? Because they can't branch to remove mate (two kings AND it'd be an inactive timeline and no other timelines to branch instead), and if they capture the rook instead, your rook from a parallel timeline can capture back. Cross-timeline defense! (If you're unconvinced, try making the capture as black and the game will point it out to you.)