# The Knight and the Maze 2

I've decided to make another knight and maze puzzle. I felt like I rushed the last one here because I thought of the idea right before the end of maze fortnight and wanted to submit something in time.

This time I've put a bit more effort in order to try and make the maze a bit more difficult. I have very much appreciated the comments and suggestions on the previous puzzle and have tried to incorporate them here. I hope you enjoy the puzzle.

To refresh, shown below is a grid of blue and white squares with a knight in the upper left hand corner and a dark green square in the lower right hand corner.

Your task is to guide the knight from its starting position to the dark green square using regulation chess knight moves.

The knight may only visit white squares to reach its goal.

• Easier solution for the green at least. Put a letter in it, like "E" or something. – dcfyj Jul 29 '16 at 12:00
• Why do I keep missing these?! :( – Jonathan Allan Jul 29 '16 at 15:26

Here are all 48 solutions to the maze with no repeated squares (shortest first):

The maze actually has some isolated or unreachable components, and one component that is isolated unless you pass through the goal cell:

• Wow, great effort. +1. So the first one looks like that given by Arth. Is that correct? – hexomino Jul 29 '16 at 13:45
• @hexomino Correct. – 2012rcampion Jul 29 '16 at 13:46
• Pumping the maze into my solver from the last one yields the same as @Arth's an optimal solution. – Jonathan Allan Jul 29 '16 at 15:27
• @Goinghamateur I updated my answer with a plot of the connected components in the maze so you can see why. – 2012rcampion Jul 29 '16 at 19:29
• I've accepted this answer because I very much like the thorough analysis, especially on which squares can/cannot be visited. – hexomino Jul 29 '16 at 21:46

If you take the directions on a clock as the possible moves, 1,2,4,5,7,8,10,11:

4,5,2,1,5,5,8,7,4,5,5,5,5,5,1,1,2,2,2,5,5,4,1,5,5,8,7,7,5,5,2,4,5,5

Will do it

Which is 34 moves in total.

• Yeah, that's the best I find too. – Florian F Jul 29 '16 at 12:58
• My computer also says that this is the shortest solution. – 2012rcampion Jul 29 '16 at 13:24

Here is a solution to the maze:

• * Here is a solution to the maze.. +1 though :P – Arth Jul 29 '16 at 12:17
• Well done. That was very quick again. You are obviously very good at these. +1 from me but I may hold out for the optimal solution for the tick. – hexomino Jul 29 '16 at 12:24
• @Arth My computer finds 48 distinct solutions that don't repeat any squares. – 2012rcampion Jul 29 '16 at 13:26