# Introducing WorDonimoes$^2$

@Don Kirkby have designed a set of dominoes puzzles that they call Donimoes. You slide the dominoes like the cars in Nob Yoshigahara's Rush Hour puzzle, always along their long axis.

I have altered this puzzle by changing numbers to letters.

## The Blocking Puzzle's Goal

The goal is to slide all the dominoes into a rectangle, without sliding any matching numbers next to each other.

## Moves

Move a domino one space along its long axis so that none of its letters match an adjacent letters on a neighbouring domino.

## Stay Connected

All the dominoes in the puzzle have to be connected in one solid group, diagonal connections don't count. When you move a domino, it can be disconnected during the move, as long as it is connected at the start and the end of the move. Remember that it can only move one space at a time, though.

## Notes

1) There may be more than one solutions. The one that I am looking for will form something special.

2) The two "CO" tiles have been named as "CO1 and CO2" for your convenience. Stay calm - they are not harmful nor toxic :P

• So I think the "special" end configuration has been identified already (by Jan Ivan) although it would seem that getting the dominoes into this configuration without breaking any rules is very difficult. I have to ask, is it definitely possible? – hexomino Aug 1 '19 at 12:14
• " it can be disconnected during the move," is confusing since you can't do it anyway. I think it is possible - I think i see it how, but it takes me too long to draw it, so I give up. – Jan Ivan Aug 1 '19 at 12:16
• It troubles me that the initial configuration has two Rs next to one another... – Gareth McCaughan Aug 1 '19 at 12:19
• @GarethMcCaughan Yes, me too (also two Ss). It feels like you're already breaking the rules before you start. My interpretation was that once you separate them they can't come back together. – hexomino Aug 1 '19 at 12:21
• That's also how I interpret it. – Gareth McCaughan Aug 1 '19 at 12:23

It's impossible.

First of all,

CO1 and ST tell us that the vertical side of the rectangle is of size at least 4.

Second,

AI, ER, IR and CO2 tell us that the other side is of size at least 4 as well. Therefore we are aiming at a 4x4 square.

Finally:

Just before you move the CO1 up (you clearly have to at some point)

$$\bullet$$ you need to have moved the other O to the left before that (there is not enough room on the right) otherwise you break the no two identical letters adjacent rule.

$$\bullet$$ you also need to have moved IR to the left (to make room for the CO1 to move up).

$$\bullet$$ you cannot possibly have moved ES up, otherwise moving CO1 would result in disconnecting ST from the rest of the board.
Conclusion: at that very moment, the block CO1 ST ES is disconnected from the other letters.

• So this is not valid? i.stack.imgur.com/NMBNz.png – Jan Ivan Aug 2 '19 at 7:36
• @JanIvan My interpretation was that the Os are the same (1 and 2 are just labels to distinguish the tiles). – hexomino Aug 2 '19 at 8:59