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Fivebyfivia Delenda Est (fivebyfivia-walkthrough.txt)

Author's Walkthrough for Fivebyfivia Delenda Est, by Andrew Schultz

There is no map for this game, or at least, I can't really make a legible one that covers all
areas and is actually helpful. The text diagrams, I hope, suffice.

The solution is not meant to be hard for chessplayers. However, non-chessplayers may find things
tricky. Note that you also have to be reasonably quick about checkmating your opponent. You only
have three turns from placing the first piece to placing the opponent's king.

You may also note there is more than one solution. Every other solution should be a rotation or
mirroring of the ones listed below.

I've included, first, diagrams, then move-by-move solutions.

Here is one solution for two rooks:

+-+-+-+-+-+
| | | | | |
+-+-+-+-+-+
| | | | | |
+-+-+-+-+-+
| | | | | |
+-+-+-+-+-+
| | |R| | |
+-+-+-+-+-+
|k| | | |R|
+-+-+-+-+-+

For the queen, there are several possibilities. But 1) she doesn't like getting too close to
the opponent's king and 2) if you do things a certain way, it disrupts the next plan.

So this is chessically correct but wrong for the game:
+-+-+-+-+-+
| | | | | |
+-+-+-+-+-+
| | | | | |
+-+-+-+-+-+
| | | |K| |
+-+-+-+-+-+
| | |Q| | |
+-+-+-+-+-+
| | |k| | |
+-+-+-+-+-+

So is this:
+-+-+-+-+-+
| | | | | |
+-+-+-+-+-+
| | | | | |
+-+-+-+-+-+
| | | |K| |
+-+-+-+-+-+
| | | | | |
+-+-+-+-+-+
| | |Q| |k|
+-+-+-+-+-+

But this is the one that you want:
+-+-+-+-+-+
| | | | | |
+-+-+-+-+-+
| | | | | |
+-+-+-+-+-+
| | | |K| |
+-+-+-+-+-+
| | | | | |
+-+-+-+-+-+
|Q| |k| | |
+-+-+-+-+-+

Note that this could also have each piece shifted to the right one column, but the more visible
mate, with just your king shifted left, would not be possible with your knight moves.

Note that you get an extra move for King and Queen vs. King, because you need the special alternate
solution.

King and rook vs king is trickier. The only way to get him in the corner with three moves is as
follows. It is one of the rejected mates above for the queen -- the one they want to save for later,
for a surprise.

+-+-+-+-+-+
| | | | | |
+-+-+-+-+-+
| | | | | |
+-+-+-+-+-+
| | | |K| |
+-+-+-+-+-+
| | | | | |
+-+-+-+-+-+
| | |R| |k|
+-+-+-+-+-+

The final quest is a traversal. You need to touch all the squares without going over one twice. This
seems like there are so many possibilities, but process of elimination helps. This is something
where hopefully you don't need mathematical proof to see it works, but you see a bunch of moves
belong together, and not much is left over.

If you need a hint, you can start in a corner and work backwards to the center.

It's a big first step to notice movement from and to the corner squares is restricted. Note
that the only way to reach a1, a5, e1, or e5 (corner squares,) you must be on c2, b3, c4 or d3
first.

Thus the following (or their reversals) must appear in the move chain, though one may be eliminated
for the final move. And they must be strung together and done all at once. Also, if a corner square
isn't the last one covered, we will get stuck at another corner square if we retro-fit where to
go.

c2-a1-b3
b3-a5-c4
c4-e5-d3
d3-e1-c2

Note also that if we do not start or end in a corner, we have a chain of 9 squares linking all above
... but if we have that, square 1 must equal square 9! So the traversal has to end in a corner.

And what's more, if we work backwards, we can see squares 23, 21, and 19 have to be, with
c2/b3/c4/d3 being in the mix.

That simplifies our map a bit. We only have 16 squares (2-17) remaining to traverse now, not
including the start.

Also, note we are guaranteed that, if we make it that far, we will be able to do the final loop in
some way. Why?

First, note each move is between a black square and white square. So square 1 is black, and square
18, where we start the end loop, is white. But all the remaining black squares (not corner or
center) have a path to one of the central white squares that start the final tour.

B W B W B
W B W B W
B W B W B
W B W B W
B W B W B

Now let's visualize where we need to get.

+-+-+-+-+-+
|x| | |2|x|5
+-+-+-+-+-+
| | |x| | |4
+-+-+-+-+-+
| |x|1|x| |3
+-+-+-+-+-+
| | |x| | |2
+-+-+-+-+-+
|x| | | |x|1
+-+-+-+-+-+
 a b c d e

Square number 2 doesn't really matter. You can always rotate or flip the chessboard so 2 winds
up at d5. (The same applies to squares 18-25. Wherever you start, you just go
corner/out/corner/out/corner/out/corner.)

From d5, then, the only viable squares are b4 and e3. Both work, providing an interesting circular
whirly motion, because all further moves are forced so as to keep squares 18-25 open. We always need
to avoid the squares listed above.

+-+-+-+-+-+
|x|c|7|2|x|5
+-+-+-+-+-+
|6|h|x|d|8|4
+-+-+-+-+-+
|b|x|1|x|3|3
+-+-+-+-+-+
|g|5|x|9|e|2
+-+-+-+-+-+
|x|a|f|4|x|1
+-+-+-+-+-+
 a b c d e

From "h" (b4) you can then jump to d3 and then clean out the corner squares.

===================================================================

Here are the move-by-move solutions, with whitespace, so they're not spoiled.












SSE.NNE.SWW.SEE.CALL ROOK (it doesn't matter which).NWW.CALL ROOK.SWW.CALL KING











SSE.CALL QUEEN.NNW.SSW.NNW.CALL KING (if you can summon your own king, the game gives him
preference).SSE.CALL KING











SWW.SEE.CALL ROOK.NNW.CALL KING.SSW.CALL KING











NNE.SSE.SSW.NWW.NNW.NEE.SEE.SSW.SWW.NNW.NNE.SEE.SSE.SWW.NWW.NNE (all but the corners and
corner-adjacent points done).SEE.SSE.NWW.SWW.NNE.NNW.SEE.NEE

Congratulations! You have won.