The answer is DES PLAINES.
The corresponding square is ILLINOIS.
by Dan Katz (with help from everyone)
Solution provided by Joseph DeVincentis:

The Duck Konundrum was a hilarious puzzle from the MIT Mystery Hunt a number of years ago which featured a complex set of rules to be followed among several players, using chairs (one of them an armchair), colored paint to paint letters on the chairs, and a duck. In 2002 there was a followup to this puzzle, using board games. The creators of this hunt failed to post a solution, but the puzzle is here. This page presents my solution.

Setup

I have gathered the following games: Clue, Scrabble, Trivial Pursuit, Chess, and Escape from Zyzzlvaria.

Oh wait, I don't seem to have Escape from Zyzzlvaria. Maybe that is because the creators of this puzzle made it up. I'll have to wing it. According to the rules, I need these spaces: Immunity Zone, Lazyr Zone, Sector J, Core Reactor, Astro Jail, Outpost 9, Sector N Reverse Dimension, and there is an unknown relationship between the board spaces. I also need some pieces: Harold (green), Ralph (orange), Leah (blue), Zoe (pink), and Captain Blastoid (metallic). I also need some dollarbucks (which are not pieces), a Moon Counter, and a Wheel of Death.

Turn 1

Each turn, I will present the action occurring on each board in a table, one game per row, with the board image/description at the end of that action and a description of the actions taken during the turn. In the last row I will indicate any end-of-turn moves, mainly the action of the duck, and show any changed gameboards. The action from each game happens simultaneously (and conditions are checked based on the conditions before any actions), but actions from one game which affect another board and actions of the duck happen at the end of the turn.


Set up the chessboard for the start of a normal game, and move each pawn once legally so that no pawn is on a square matching its color.

Spell NORTH, SOUTH, EAST, WEST at the appropriate ends of the center column and row. Put an X on the center square.

For reference:
Letter values: A:1 B:3 C:3 D:2 E:1 F:4 G:2 H:4 I:1 J:8 K:5 L:1 M:3 N:1 O:1 P:3 Q:10 R:1 S:1 T:1 U:1 V:4 W:4 X:8 Y:4 Z:10
Initial letter distribution: A:9 B:2 C:2 D:4 E:12 F:2 G:3 H:2 I:9 J:1 K:1 L:4 M:2 N:6 O:8 P:2 Q:1 R:6 S:4 T:6 U:4 V:2 W:2 X:1 Y:2 Z:1 blank:2
Remaining letters: A:8 B:2 C:2 D:4 E:10 F:2 G:3 H:0 I:9 J:1 K:1 L:4 M:2 N:5 O:6 P:2 Q:1 R:5 S:1 T:2 U:3 V:2 W:1 X:0 Y:2 Z:1 blank:2
Harold: Immunity Zone
Ralph,Leah: Lazyr Zone
Zoe: Sector J
Captain Blastoid: Core Reactor
Place Harold on the Immunity Zone, Ralph and Leah on the Lazyr Zone, Zoe on Sector J, and Captain Blastoid on the Core Reactor.

Place each pie on the wedge space on the opposite side of the board from the wedge space matching the color of the pie. (Since the rules don't seem to care about the arrangement of the wedges, I am using some rather non-standard looking pies to make the graphics easier to draw.)

Place each character in a different room, starting in the Conservatory and proceeding clockwise, in alphabetical order by last name of the actor who played them in the movie Clue. This order is: Brennan (Peacock), Kahn (White), Lloyd (Plum), McKean (Green), Mull (Mustard), and Warren (Scarlet).

Of the three empty rooms (Ballroom, Kitchen, Dining Room), place the Wrench and Gun in the smallest room (clearly the Kitchen), the Rope and Knife in the room that comes first alphabetically (Ballroom), and the Lead Pipe and Candlestick in the third room.

None of the conditions for the Duck to act are satisfied at this point.

Turn 2


Make the four legal, non-en-passant captures. Then make a legal move with each knight, choosing the square closest to h1 is there are multiple choices.

WQxP(h5), BQxP(h4), WBxP(b5), BBxP(b4)
WN-d2, BN-d7, WN-h3, BN-h6.

Four tiles are between pairs of DLS squares. Place tiles on each of the eight DLS squares to make four runs of three consecutive letters, reading left-to-right and/or top-to-bottom, treating ZA as a consecutive pair. This occurs at the third letter from each edge, so we form the sequences QRS, RST, ZAB, and TUV.

For reference:
Letter values: A:1 B:3 C:3 D:2 E:1 F:4 G:2 H:4 I:1 J:8 K:5 L:1 M:3 N:1 O:1 P:3 Q:10 R:1 S:1 T:1 U:1 V:4 W:4 X:8 Y:4 Z:10
Remaining letters: A:8 B:1 C:2 D:4 E:10 F:2 G:3 H:0 I:9 J:1 K:1 L:4 M:2 N:5 O:6 P:2 Q:0 R:4 S:0 T:0 U:3 V:1 W:1 X:0 Y:2 Z:0 blank:2
Harold, 3 Dollarbucks: Immunity Zone
Ralph,Leah, 8 Dollarbucks: Lazyr Zone
Zoe, 3 Dollarbucks: Sector J
Captain Blastoid, 3 Dollarbucks: Core Reactor
Moon Counter: Last Quarter
Place 3 dollarbucks on the same area as each character, unless there are 2 characters in an area in which case put 8 dollarbucks there.  Set the Moon Counter to Last Quarter.

Move each pie clockwise the same number of spaces as there are letters in the name of the pie's color. (Colors are green, pink, brown, orange, blue, yellow.) Move any pie that lands on Roll Again the same number of spaces again.

Switch the contents of each pair of rooms that are connected by secret passages. Take the two characters of the same gender who are in adjacent rooms and move them to the Hall. (Note that Scarlet, White, and Peacock are female, so this (after the swap) is Scarlet and White.

Harold, Mrs. White, 3 Dollarbucks: Immunity Zone
Ralph,Leah, 8 Dollarbucks: Lazyr Zone
Zoe, 3 Dollarbucks: Sector J
Captain Blastoid, 3 Dollarbucks: Core Reactor
Moon Counter: Last Quarter
The queens are on adjacent squares, so the white queen moves to the square opposite the one it is currently on (reflected through the center of the board).
Three Clue characters are in the same room, so the one whose last name comes alphabetically last (White) moves to the Immunity Zone.

Turn 3

Remove from the board any piece currently threatened by a piece in the lower left quadrant of the board. This means:
BB(b4) (attacked by pawns and queen)
WP(a3) (attacked by bishop)
WP(c3) (attacked by bishop)
BP(a6) (attacked by queen)

Move every piece in the 6th rank down one space.
BP-c5, BP-e5, BP-g5, BN(h6)-h5

Spell the word TONE using a T already on the board in every place where this is a legal move. Replace each T that you cannot use in this way with a G. (Since SO is a legal word but VO is not, this is possible everywhere except for the two Ts nearest to the bottom.) Interestingly, the replacements have made the legal words GUV and SOUGH.

For reference:
Letter values: A:1 B:3 C:3 D:2 E:1 F:4 G:2 H:4 I:1 J:8 K:5 L:1 M:3 N:1 O:1 P:3 Q:10 R:1 S:1 T:1 U:1 V:4 W:4 X:8 Y:4 Z:10
Remaining letters: A:8 B:1 C:2 D:4 E:6 F:2 G:1 H:0 I:9 J:1 K:1 L:4 M:2 N:1 O:3 P:2 Q:0 R:4 S:0 T:2 U:3 V:1 W:1 X:0 Y:2 Z:0 blank:2
Harold, 3 Dollarbucks: Immunity Zone
8 Dollarbucks: Lazyr Zone
Zoe, 3 Dollarbucks: Sector J
Captain Blastoid, 3 Dollarbucks: Core Reactor
Ralph,Leah: Astro Jail
Mrs. White: Outpost 9 or Sector N
Moon Counter: Last Quarter
Take every character on the area with the most dollarbucks and move it to the Astro Jail (Ralph, Leah).
If Captain Blastoid is less than five squares away from Zoe, move a piece which is sharing an area with Harold to Outpost 9; otherwise move it to Sector N. (We don't know how far the pieces are apart, so Mrs. White moves to an indeterminate place)

For each pie, put in a wedge of each color such that the pie is exactly five squares away from a space of that color.
Green gets blue
Brown gets orange
Blue gets blue, yellow
Orange gets blue, orange, green
Yellow gets yellow, orange, brown
Pink gets pink, brown

Two pies now have wedges of the same color as the space the pies are now on. (Blue, Pink). Move each of those pies to the nearest wedge space and three spaces inward.
Move every nonmetallic weapon one room counterclockwise. (Only the Rope is nonmetallic.)
If Professor Plum is in a room with a weapon, place it in the kitchen; otherwise, place the Candlestick in the same room as Plum. (He is not in a room with a weapon, so the Candlestick moves to the Library.)

The duck is idle this turn.

Turn 4

If one white piece is removed, the piece on c1 can move to the 8th rank in three moves without making any captures. (This is the white knight on b4.) Remove that piece and place it on f6. (The black king is in check.)

Then move the piece on c1 three times to take it to the 8th rank (WB-b4-a5-d8).

Use the piece on h4 to capture the most powerful piece it currently threatens. BQxWN(h3).

Move every A, B, C, D, and E one square down and to the left. (one A, one B, and six Es are affected.)

Switch the positions of the two consonants which are now one square up and one to the left of a TLS square. (The N at e9 and the V at I13.)

The movement made quite a mess, but the swap has notably formed the word GUN.

For reference:
Letter values: A:1 B:3 C:3 D:2 E:1 F:4 G:2 H:4 I:1 J:8 K:5 L:1 M:3 N:1 O:1 P:3 Q:10 R:1 S:1 T:1 U:1 V:4 W:4 X:8 Y:4 Z:10
Remaining letters: A:8 B:1 C:2 D:4 E:6 F:2 G:1 H:0 I:9 J:1 K:1 L:4 M:2 N:1 O:3 P:2 Q:0 R:4 S:0 T:2 U:3 V:1 W:1 X:0 Y:2 Z:0 blank:2
Harold, 3 Dollarbucks: Immunity Zone
5 Dollarbucks: Lazyr Zone
Zoe, 1 Dollarbuck: Sector J
Captain Blastoid, 3 Dollarbucks: Core Reactor
Mrs. White: Outpost 9
5 Dollarbucks: Sector N
Ralph,Leah: Astro Jail
Moon Counter: Last Quarter
Move 2 dollarbucks from the area Zoe is on and 3 from the Lazyr Zone to Sector N.

Move all characters on Sector N to Outpost 9. (Mrs. White's location is now certain.)

Put the brown pie halfway between where it is now and where the orange pie is. Put the blue pie halfway between where it is now and where the pink pie is.
Place the weapon that is in the same room as the character who is a Reverend in Cluedo on the Stairway. (Character is Green, so this is the Rope.)

Move the character closest to the Billiard Room into the Dining Room. (This is Professor Plum.)


GUN was spelled on the Scrabble board, so the Gun moves from the Study to J13 on the Scrabble board.
The blue pie is on the hub, so the blue Zyzzlvaria piece (Leah) moves to the hub.



Harold, 3 Dollarbucks: Immunity Zone
5 Dollarbucks: Lazyr Zone
Zoe, 1 Dollarbuck: Sector J
Captain Blastoid, 3 Dollarbucks: Core Reactor
Mrs. White: Outpost 9
5 Dollarbucks: Sector N
Ralph: Astro Jail
Moon Counter: Last Quarter

Turn 5

Castle as both black and white, one king-side and one queen-side. (Since there are pieces in the way on the queen-side of the black king, do the king-side castling for black. Black remains in check.)

Legally capture a piece that cannot move diagonally with a rook.
BR(f8)xf6, breaking the check.

Remove every piece that is currently threatened by two pawns. This is:
BP(e5) - threatened by d4 and f4
WP(d4) - threatened by c5 and e5
WP(f4) - threatened by e5 and g5
Legally play four of the following words, placing only ten tiles: AXED, BRAIN, CROWN, SOUP, STAKE, and WASTE.
This is WASTE across 8a, SOUP down I3, STAKE down N8, and AXED across 8G (or possibly across 12A or 12L using a blank for the X, but for now assume no blank is used.)

Place a U in every empty square immediately to the left of an A, unless it is on the left half of the board. (Only two As have empty squares to the left, the ones at G8 and N10, and the one at G8 is in the left half of the board.)

For reference:
Letter values: A:1 B:3 C:3 D:2 E:1 F:4 G:2 H:4 I:1 J:8 K:5 L:1 M:3 N:1 O:1 P:3 Q:10 R:1 S:1 T:1 U:1 V:4 W:4 X:8 Y:4 Z:10
Remaining letters: A:5 B:1 C:2 D:3 E:4 F:2 G:1 H:0 I:9 J:1 K:0 L:4 M:2 N:1 O:3 P:1 Q:0 R:4 S:0 T:1 U:1 V:1 W:1 X:0 Y:2 Z:0 blank:2
Harold, 3 Dollarbucks: Immunity Zone
5 Dollarbucks: Lazyr Zone
Zoe, 1 Dollarbuck: Sector J
7 Dollarbucks: Core Reactor
Mrs. White, Captain Blastoid: Outpost 9
5 Dollarbucks: Sector N
Ralph: Astro Jail
Moon Counter: Last Quarter
Since no area with an even, non-zero number of dollarbucks exists, move Captain Blastoid to the westernmost area which contains a character from another game (only Mrs. White is here, in Outpost 9).

Add 4 dollarbucks on the Core Reactor.
Move each piece on the board to the space closest to the hub which is the same color as the space the piece is currently on. If a piece is already on the hub, move it to the wedge space of the color opposite the color of the piece on a standard color wheel.
(The blue hub and Leah move to the orange wedge space.)
Move each weapon (except the one on the stairway) clockwise two rooms, unless the weapon's name contains a K, in which case move it two rooms counterclockwise. (The Knife and Candlestick contain Ks. The gun is not in a room, nor in a place where is can move clockwise or counterclockwise, so it does not move.)

Move Mr. Green to the only empty room that has a secret passage. (The Study)


The duck is idle this turn.

Turn 6

Perform all possible one-move captures by bishops and knights.
WB(d8)xf6
WB(b5)xd7
BN(h5)xg3

Move the white king to any square on the 8th rank horizontally adjacent to two black pieces.
WK-b8 (and he is in check there, but again we don't care).
Put an I in every empty DLS that is orthogonally adjacent to at least two tiles. (I7 and M9)

Place an O four spaces to the right and one space up from the place where you could put an R to complete a 7-letter word. (That is SOUPIER, R at I9, so it goes at M8. This also confirms AXED is in the right place; if it went in either other place, you would not be able to form a seven letter word by adding an R.)

Put an I in every empty DLS that is orthogonally adjacent to at least two tiles. Again. (L8 this time)

For reference:
Letter values: A:1 B:3 C:3 D:2 E:1 F:4 G:2 H:4 I:1 J:8 K:5 L:1 M:3 N:1 O:1 P:3 Q:10 R:1 S:1 T:1 U:1 V:4 W:4 X:8 Y:4 Z:10
Remaining letters: A:5 B:1 C:2 D:3 E:4 F:2 G:1 H:0 I:6 J:1 K:0 L:4 M:2 N:1 O:2 P:1 Q:0 R:4 S:0 T:1 U:1 V:1 W:1 X:0 Y:2 Z:0 blank:2
Harold, 3 Dollarbucks: Immunity Zone
5 Dollarbucks: Lazyr Zone
Zoe, 1 Dollarbuck: Sector J
7 Dollarbucks: Core Reactor
Mrs. White, Captain Blastoid: Outpost 9
Ralph,5 Dollarbucks: Sector N
6 dollarbucks: Astro Jail
Moon Counter: Eclipse
Put 6 dollarbucks on the Astro Jail. Set the Moon Counter to Eclipse. Move all characters currently on the Astro Jail to Sector N (Ralph).

Move Zoe to the same space as Leah. Move Leah one space clockwise for every dollarbuck on Sector N. Since Leah is on the Trivial Pursuit board, these actions happen at the end of the turn.
Move each pie (4-N) spaces, where N is the number of wedges in that pie, without passing through or landing on the hub or a Roll Again space. (Blue moves inward, others move outward. Leah is not a pie and does not move.)

If a pie does not contain the wedge of the color of the space it is now on, add that wedge.
Brown gets blue
Pink gets blue
Green gets pink
Blue gets brown

Also add a blue wedge to the yellow pie.
Since there are more black knights than white knights on the chessboard (checked at beginning of turn, so 2 vs. 0), switch the positions of Colonel Mustard and the Rope.

Place the weapon currently in Miss Peacock's room on the hub of the Trivial Pursuit board. (The Wrench. It moves at end of turn since it affects another board.)

Harold, 3 Dollarbucks: Immunity Zone
5 Dollarbucks: Lazyr Zone
1 Dollarbuck: Sector J
7 Dollarbucks: Core Reactor
Mrs. White, Captain Blastoid: Outpost 9
Ralph,5 Dollarbucks: Sector N
6 dollarbucks: Astro Jail
Moon Counter: Eclipse

Take care of the end of turn actions from the games:
Move Zoe to the same space as Leah. Move Leah one space clockwise for every dollarbuck on Sector N (5). Place the Wrench on the hub of the Trivial Pursuit board.

Duck actions:
Since all six pies have a blue wedge, place the blue Clue piece -- Miss Peacock -- on the chessboard one square to the right of the black king. (in h8)
There is a 2x2 square of vowels on the Scrabble board so replace the Is at L8 and M9 with Ls. (Remaining letters include I:8 and L:2)



Turn 7

Switch these pieces: the black piece orthogonally or diagonally adjacent to two white pieces (BB, c8) and the piece which is next to a piece which is neither black nor white (BK, g8, next to Miss Peacock).

Since the position (ignoring Miss Peacock) could not occur in a legal game (since the kings are adjacent), move all knights on the board into the Hall (just the BN on g3, and it happens at the end of the turn).
Move the 12-tile island (with WASTE) up and right one square.

Move the one-tile island (the loose E) to the space above the rightmost single tile with the highest point value (so to M6, above the Z).

For reference:
Letter values: A:1 B:3 C:3 D:2 E:1 F:4 G:2 H:4 I:1 J:8 K:5 L:1 M:3 N:1 O:1 P:3 Q:10 R:1 S:1 T:1 U:1 V:4 W:4 X:8 Y:4 Z:10
Remaining letters: A:5 B:1 C:2 D:3 E:4 F:2 G:1 H:0 I:8 J:1 K:0 L:2 M:2 N:1 O:2 P:1 Q:0 R:4 S:0 T:1 U:1 V:1 W:1 X:0 Y:2 Z:0 blank:2
Harold, 3 Dollarbucks: Immunity Zone
5 Dollarbucks: Lazyr Zone
1 Dollarbuck: Sector J
7 Dollarbucks: Core Reactor
Mrs. White, Captain Blastoid: Outpost 9
Ralph,5 Dollarbucks: Sector N
6 dollarbucks: Astro Jail
Moon Counter: Eclipse
Since the duck has not yet laid an egg, switch the positions of Leah and Captain Blastoid. (Since Leah is on the Trivial Pursuit board, this happens at the end of the turn.)
Since the hub is not empty, place the piece closest to the Orange wedge space onto square g2.
(This is Zoe, who is actually on the orange wedge. I assume this is the chess square g2, not the Scrabble one, since they bothered to define notation only for the chess board. Since g2 is on the chessboard, this happens at the end of the turn. Nothing actually happens in this phase.)
Moving all the weapons one room clockwise would put the knife in the Kitchen, so move all the pieces from the Study into the Library (Mr. Green).

Moving all the weapons one room counterclockwise would not put a weapon into a room that starts with the same letter, so do nothing else.


Take care of the end-of-turn actions from the games:
Move the black knight into the Hall.
Switch Leah and Captain Blastoid.
Move Zoe to g2 on the chessboard.

Duck Actions:
Since the kings are on adjacent squares, move the white queen to the opposite square (WQ-h5).
OVA was spelled on the Scrabble board this turn, so the duck lays an egg.

Harold, 3 Dollarbucks: Immunity Zone
5 Dollarbucks: Lazyr Zone
1 Dollarbuck: Sector J
7 Dollarbucks: Core Reactor
Mrs. White, Leah: Outpost 9
Ralph,5 Dollarbucks: Sector N
6 dollarbucks: Astro Jail
Moon Counter: Eclipse


Turn 8

Remove all adjacent pairs of pieces of the same type (even if not the same color). This removes both kings and two pairs of black pawns.

Make the only legal move of a black piece to the 1st rank without capturing. (BR-a1)
There is a PIE on the board, and since it doesn't specify color, I have to choose black or yellow. (Move the yellow pie to O1 at the end of the turn since it is on the trivial pursuit board now.)

Since GUN is still on the board, move the gun to the lower left square A15.

Play FAMKA across at K11, ignoring the nonsense crossing words.

For reference:
Letter values: A:1 B:3 C:3 D:2 E:1 F:4 G:2 H:4 I:1 J:8 K:5 L:1 M:3 N:1 O:1 P:3 Q:10 R:1 S:1 T:1 U:1 V:4 W:4 X:8 Y:4 Z:10
Remaining letters: A:3 B:1 C:2 D:3 E:4 F:1 G:1 H:0 I:8 J:1 K:0 L:2 M:1 N:1 O:2 P:1 Q:0 R:4 S:0 T:1 U:1 V:1 W:1 X:0 Y:2 Z:0 blank:2
Harold, 3 Dollarbucks: Immunity Zone
5 Dollarbucks: Lazyr Zone
1 Dollarbuck: Sector J
7 Dollarbucks: Core Reactor
Mrs. White, Leah: Outpost 9
Ralph,5 Dollarbucks: Sector N
9 dollarbucks: Astro Jail
Moon Counter: Eclipse
Since there are not more dollarbucks on Sector N than on the Core Reactor, add as many dollarbucks on the Astro Jail as there are bishops on the chessboard (3).
Move every piece on the board (except ones on the hub) 9 spaces, outward if possible, otherwise clockwise if the piece contains three or more wedges, and counterclockwise if it doesn't.

Put a green wedge in every pie that is now on a wedge space. (Blue, Green, and Brown)
Using common occupational gender stereotypes, move every male piece in the Hall to the kitchen (the black knight), move every female piece in the Hall to the Billiard Room (Miss Scarlet), and move every noinliving piece in the Hall to the Lazyr Zone. (The Rope moves to the Lazyr Zone at the end of the turn.)




Take care of the end-of-turn actions from the games:
Move the yellow pie to O1 on the Scrabble board.
Move the rope to the Lazyr Zone.

Duck actions: Since three rooks have moved, place the fourth one (the white rook on h1) in the Lounge.




Harold, 3 Dollarbucks: Immunity Zone
Rope, 5 Dollarbucks: Lazyr Zone
1 Dollarbuck: Sector J
7 Dollarbucks: Core Reactor
Mrs. White, Leah: Outpost 9
Ralph,5 Dollarbucks: Sector N
9 dollarbucks: Astro Jail
Moon Counter: Eclipse

Turn 9

Temporarily treat any non-chess pieces on the board as black knights. If any of them can capture, they do so.

Zoe x e3

Move each rook up as many spaces as there are Rs on the Scrabble board. (2)

BR-a3
WR-d3
Note the two tiles on the board besides Q with the highest point values (X:8 and Z:10). There are two spaces which are in the same row as one of these and the same column as the other (H7 and M8).

One of these spaces has a tile on it. Move this tile to the other space (O at M8 moves to H7) and (since there is a weapon on the board) replace it with a P.

For reference:
Letter values: A:1 B:3 C:3 D:2 E:1 F:4 G:2 H:4 I:1 J:8 K:5 L:1 M:3 N:1 O:1 P:3 Q:10 R:1 S:1 T:1 U:1 V:4 W:4 X:8 Y:4 Z:10
Remaining letters: A:3 B:1 C:2 D:3 E:4 F:1 G:1 H:0 I:8 J:1 K:0 L:2 M:1 N:1 O:2 P:0 Q:0 R:4 S:0 T:1 U:1 V:1 W:1 X:0 Y:2 Z:0 blank:2
Harold, 3 Dollarbucks: Immunity Zone
5 Dollarbucks: Lazyr Zone
Rope, 1 Dollarbuck: Sector J
7 Dollarbucks: Core Reactor
Mrs. White, Leah: Outpost 9
Ralph,5 Dollarbucks: Sector N
9 dollarbucks: Astro Jail
Moon Counter: Eclipse
Since the total number of dollarbucks on the board is even, move all pieces except people to Sector J. (The Rope moves.)
Place a yellow wedge in each pie that is one space away from a yellow space. (Orange gets a yellow wedge.)

Switch the two pies on the board that contain the most wedges (Orange and Blue; Yellow also has 4 wedges but is not on the board).

If there is a piece on the hub, switch it with the piece furthest away from the pink wedge space (wrench and Captain Blastoid swap).
Place an unused Scrabble C tile in every empty room (Study and Hall). Remaining tiles now includes C:0.

Switch the positions of the lead pipe and the wrench (at end of turn, since the wrench is on the Trivial Pursuit board).

The items in the Study and Lounge together form a word that describes the person in the Billiard Room. (C + rook = crook, describing Miss Scarlet).



Take care of end-of-turn actions from the games:
Switch the Lead Pipe and the Wrench.

Duck actions:
Plum was spelled on the Scrabble board this turn, so Professor Plum moves to M12.


Turn 10

Move every black rook to the highest rank that contains no pieces, staying in the same file.
BR-a4

Since the white queen threatens a non-chess piece, she does not capture.
Replace every tile with a point value divisible by 4 with an E, since the upper right square is not empty. These replace the H at H5, the W at B7, the V at F4, the X at H8, the F at K11, and the H at H15. Since there are only 4 Es left, two blanks must be used to accomplish this.

Place the replaced tiles in the top row in alphabetical order starting from the upper left corner. (FHHVWX)

For reference:
Letter values: A:1 B:3 C:3 D:2 E:1 F:4 G:2 H:4 I:1 J:8 K:5 L:1 M:3 N:1 O:1 P:3 Q:10 R:1 S:1 T:1 U:1 V:4 W:4 X:8 Y:4 Z:10
Remaining letters: A:3 B:1 C:0 D:3 E:0 F:1 G:1 H:0 I:8 J:1 K:0 L:2 M:1 N:1 O:2 P:0 Q:0 R:4 S:0 T:1 U:1 V:1 W:1 X:0 Y:2 Z:0 blank:0 (blanks represent 2 Es)
Harold (case 1), 3 Dollarbucks: Immunity Zone
5 Dollarbucks: Lazyr Zone
Rope, 1 Dollarbuck: Sector J
7 Dollarbucks: Core Reactor
Mrs. White, Leah: Outpost 9
Ralph,5 Dollarbucks: Sector N
9 dollarbucks: Astro Jail
Moon Counter: Eclipse (case 2) or Neutral (case 1)
Spin the Wheel of Death. If you get a skull, set the Moon counter to Neutral; otherwise, remove Harold from the board. There is no way to determine which result occurs so both are reflected on the board.
Since the duck has laid an egg, move the brown pie one space clockwise and remove the pink pie from the board.
Place the darkest-colored piece on the board to the same space Mrs. White is on. (This is Outpost 9, and the black knight moves there at end of turn.)

The wrench is removed from the board.
Harold (case 1), 3 Dollarbucks: Immunity Zone
5 Dollarbucks: Lazyr Zone
Rope, 1 Dollarbuck: Sector J
7 Dollarbucks: Core Reactor
Mrs. White, black knight, Leah: Outpost 9
Ralph,5 Dollarbucks: Sector N
9 dollarbucks: Astro Jail
Moon Counter: Eclipse (case 2) or Neutral (case 1)

Take care of end-of-turn actions from the games:
Move the black knight from the Clue board to Outpost 9.

Duck actions:
Replace the upper left and lower right vowels from the 2x2 square on the Scrabble board with Ls. (H7 and I8). (Remaining tiles include L:0 and 1 E or blank)



Endgame

Starred instructions at the end of the game rules tell us letters to extract from various games.
  1. The first letter of the answer is the file of the only white piece on the chessboard that currently threatens two black pieces. (The white bishop at d7, so D)
  2. The 2nd letter of the answer is the letter which must be represented by a blank on the Scrabble board. (E)
  3. The 3rd letter of the answer is the letter of the space containing a weapon on the Trivial Pursuit board, labeling the pink wedge space as A and proceeding counterclockwise. (S)
  4. The 4th letter of the answer is the initial letter of the last name of the suspect currently closest to the gun (Professor Plum on the Scrabble board). (P)
  5. The 5th letter of the answer is the initial letter of the Zyzzlvarian character on the same area of the board as a chess piece (Leah, so L)
  6. The 6th letter of the answer is the Scrabble tile 3 to the right and 3 down from an L which is 1 square up and 1 left from an empty square. (This is the L tile at I8, so we end up L11 which contains an A)
  7. The 7th letter of the answer is the Nth letter of the alphabet, where N is the product of the numbers of dollarbucks on the Astro Jail and the area containing a weapon (1x9 = 9, so I)
  8. The 8th letter of the answer is the letter of the space containing the brown pie. (N)
  9. The 9th letter of the answer is the file of the piece on the chess board whose name comes last in alphabetical order (Zoe, so E)
  10. The 10th letter of the answer is the initial of the last name of the suspect who has been revealed as dishonest (Miss Scarlet, so S).
And the final answer is DES PLAINES, a city in Illinois, so it corresponds with Illinois Avenue on the Monopoly board in the Monopoly meta-game running through this Mystery Hunt.