# Monday's Mirror Donimoes Problem

Help four ghosts find each other in a haunted house. I just finished adding a new puzzle to Donimoes, my collection of domino puzzles and games, so I thought I would post a few bonus problems here. The puzzle is Mirror Donimoes, and the ghosts are four pawns that walk around on top of the dominoes, trying to find each other. Each domino is a room in the house, and the ghosts can't go through the closed doors. They can go through the mirrors, though. Spooky!

## Goal

Move all the pawns into one connected group. Diagonal connections don't count.

## Start

Place the dominoes in the starting position shown in the problem, then put a pawn on top of each corner space.

## Moves

Each turn, you can make a domino move or a pawn move.

### Domino Moves

The house is so spooky, the rooms can move. If a domino has one or two pawns on it, you can slide the domino one space along its long axis. The pawns go along for the ride. You can only move one domino at a time, and all the dominoes must stay connected in one group before and after the move. Diagonal connections don't count.

Remember, a domino with no pawns on it cannot move.

### Pawn Moves

The ghosts can always move around the room, and they can move through mirrors to the room next door. You can move a pawn one space up, down, or sideways, with a few restrictions.

• Two pawns can't be on the same space, but you can have a pawn at each end of a domino.
• Moving to a neighbouring domino is only allowed if the number you move to matches the number you were on. (There's a mirror for the ghost to go through.)
• Pawns have to stay on top of the dominoes - no leaving the house.
• Diagonal moves are not allowed.

## Example

As a warm up, here's a tiny problem and its solution. First, set up the dominoes as shown in the starting position.

Then put a pawn on each corner. You can use four identical pawns, but for this example and for writing out a solution, use a regular (P)awn, a (B)ishop, a k(N)ight, and a (R)ook as four different types of pawn, so you can keep track of which is which. The small white dots show you the number under each pawn.

In this position, none of the numbers match their neighbours, so there are no mirrors for the pawns to move between dominoes. However, the 2 under the bishop could match the 2 in the middle, so the first move is to slide the bishop's domino down.

Now that there's a mirror to move through, the bishop can move to the left.

The last move is to join the ghosts into a single, connected group, and there are two choices. We can just move the rook to the other end of its domino, or we can slide the rook's domino back up, and the rook comes along for the ride.

## Solutions

To describe a solution, the pawn in the top left is labelled as a regular (P)awn, the bottom left is a k(N)ight, the top right is a (B)ishop, and the bottom right is a (R)ook. Each pawn move has two letters and each domino move has three letters.

• The first letter identifies the pawn that will move or one of the pawns on the domino that will move.
• For a domino move, the second letter is "d" for (d)omino.
• The last letter shows the direction: (L)eft, (R)ight, (U)p, or (D)own.
• If the move gets repeated, there's a number to show how many times.

For the small example above, the solution is written as "BdD, BL, RdU", which means bishop's domino down, bishop left, rook's domino up.

# Today's Problem

Here's a slightly larger problem to solve for today. Try it out, and post your solution.

If you like this puzzle, watch for more challenging problems later in the week.

• Nice puzzle! Two questions: (1) (for the sake of moves counting) do subsequent repeated moves count for one move? For example: does BdD3 count for 1 or for 3 moves? And (2) does the house need to be left in a nice rectangular shape at the end? Jun 25, 2020 at 10:11
• Cool puzzle - and very cool webpage. Something added to my bookmarks now :c) Jun 25, 2020 at 11:52
• BdD3 counts as 3 moves, @melfnt, and the house can be in any shape at the end, so long as it's always in one connected group of dominoes. Jun 25, 2020 at 14:03

My solution takes 18 moves. Shaded areas denotes the presence of a ghost (click on the text to keep the spoilers open).

First half

We need a "driver" for the 2/0 room: the rook will do it.

Second half

The rook rescues the pawn, then all the ghosts meet at the bottom-right corner.

Sorry for the ugly libreoffice screenshots, here is a transcription:

PD, BD, NR, RL, NdL, RdL

PdU, RU

RdL2

PD

RdR2

RD, RR, PL, PD

BdD

I have the following solution:

Red dots denote ghosts. The tricky part is the last few moves, where you have to be careful to keep the dominos connected.

• Ninja'd me! I was typing up a (different) solution when I saw this :( Jun 22, 2020 at 16:08
• Did your solution use fewer moves, @bobble? Jun 23, 2020 at 2:40
• Yes, but only by a little. Do you want me to post it @DonKirkby? Jun 23, 2020 at 14:42
• Sure, @bobble, I'd love to see another solution. Jun 23, 2020 at 19:45

My (slightly shorter) solution, as requested by OP. The ghosts are indicated by capital letters in the bottom left corner of their spot.

• Very nice! I wonder if anyone can solve it in even fewer moves. Jun 24, 2020 at 4:46