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Today is the start of NaNoWriMo (National Novel Writing Month), and I wanted to come up with some type of a puzzle to celebrate. I think this is a new style of puzzle (if it's not, please let me know!) and I'm not 100% confident in what's truly the most optimal solution. With that said, onto the puzzle!

The letters of NaNoWriMo have been jumbled up and put into a 3x3 grid in alphabetic order. Your job is to reassemble them in the proper order when read left to right, top to bottom in as few moves as possible. One move counts as any of the following items:

  • Swapping any two adjacent pieces
  • "Connecting" any two adjacent pieces. All pieces that are connected move together with a single move.
  • Break off a piece that is connected to other piece(s)

To provide an example, say the "letters" were A,B,C,D in a 2x2 grid. If the goal was to get B,A,D,C you could do that in two moves. Swap the A and the B, then swap the C and the D. If the goal was to get C,D,A,B you could also do that in two moves by using the first move to connect either the A,B or the C,D and then the second move to swap the connected two pieces with their adjacent pieces. If the goal was to get C,D,B,A that would take at least three moves. Do the two moves as above (being sure to connect C,D and not A,B) to get C,D,A,B then use a third move to swap the unconnected A,B.

Picture of the examples:

Picture of examples

Blue highlighted cells are "connected", red text in the cell indicates that that letter was moved that turn. Hopefully this helps clear up.

Any number of pieces can be connected, not just two, but each connection costs a move. If a non-rectangular piece is created it would move like this: Assume A, B, and D are connected. Moving that set of pieces would take the grid from:

A  B  C
D  E  F
G  H  I

to:

C  A  B
E  D  F
G  H  I

Note the connected cells ABD remain their exact shape when they move together.

The letters A,I,M,N,N,O,O,R,W in a 3x3 grid

Text version of the puzzle grid:

A  I  M
N  N  O
O  R  W

You want to use as few moves as possible to put the letters in order:

N  A  N
O  W  R
I  M  O

I completed in 8 moves. Can you find a more optimal solution?

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  • $\begingroup$ @Christoph Yes, more than 2 pieces can be connected, but each connection is a move. When swapping a non-rectangular piece, I will add an example showing that as well $\endgroup$
    – Anthony Ingram-Westover
    Nov 1, 2020 at 15:56
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    $\begingroup$ I added an example with a three connected non-rectangular piece. It moves as a single piece so it maintains the shape of the connected pieces. $\endgroup$
    – Anthony Ingram-Westover
    Nov 1, 2020 at 16:00

1 Answer 1

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I have not yet been able to beat an 8-move solution, only match it



 A   I   M

 N   N   O

 O   R   W


1. 


 A   I - M

 N   N   O

 O   R   W


2. 


 I - M   A

 N   N   O

 O   R   W


3. 


 I - M   O

 N   N   A

 O   R   W


4. 


 I - M   O

 N   A   N

 O   R   W


5. 


 I - M - O

 N   A   N

 O   R   W


6. 


 I - M - O

 N   A   N

 O   W   R


7. 


 N   A   N

 I - M - O

 O   W   R


8. 


 N   A   N

 O   W   R

 I - M - O

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