# Number maze with a rule on it

The rules are:

• You start at 1
• No diagonal moves, and you must move 1 step at a time
• You must follow this pattern: $a < b > c < d > ...$ (assuming letters are numbers)
• Do you have to go across every number as well? – Beastly Gerbil Jul 9 '18 at 6:20
• @BeastlyGerbil It's a maze, so I guess not. Just reach the end. – Jelmer Jul 9 '18 at 6:36
• @BeastlyGerbil No. – u_ndefined Jul 9 '18 at 6:46

Since we alternate between increasing and deceasing, we can color the maze like a checkerboard, where we alternate between black and white. This means that whenever we go from black to white we always have to increase, and when we go from white to black we always have to decrease (or vice versa, depending on your coloring).

If something is increasing in one direction, it is decreasing in the opposite direction. So we can always either go both directions between 2 spaces, or are blocked between 2 spaces. Equal numbers are neither increasing nor decreasing, so we cannot move between those.

With this information, all the walls in the maze are static. Therefore it's possible to draw them in, which I've done.

At this point it's easy to see the path through (assuming I haven't made any mistakes).

The diagonal path means you can go through there in any order.

• this is amazing. – u_ndefined Jul 9 '18 at 15:02
• Very clever idea to correlate to a checkerboard. And a very useful image. +1 – CiaPan Jul 10 '18 at 13:09

My first try, there's probably a quicker route ^_^

I hope this is the fastest route:

total : 30 steps