I stumbled upon this maze idea last night after I was working on a maze based on a Karnaugh diagram. I realized that that would be too difficult to follow, and that this new maze has some interesting properties.

Here's how it works:

There's an NxN grid of ones and zeroes (in this case, 4x4), and the grid is subdivided into smaller grids (in this case, four 2x2's). You can move from one number to an adjacent number, or from one position in a grid to its relative position in an adjacent grid. (From the top-left of one big square to the top-left of an adjacent square, for example.)

Here's the catch, a move is only legal if the number of the square you're on and the number of the square you're going to are different!

The large grid move allow a parity change that makes the puzzle interesting. The grid needs to be in the order of (Nx4)x(Nx4) to allow the parity changing moves.

To solve the puzzle below, you must get from one corner to the opposite corner. All squares are reachable, although it may not seem that way while you're traversing it!

Can you think of a good name for this maze? How about making an 8x8 version?

I have a question about the legality of a move. So you can only move from a 0 to a 1, or vice versa. Also, you must move left, right, up, down, or to a relative position in a different square.

Can you move from the 1 in the upper-left of the lower left box up to the 0 in the lower-left of the upper-left box (or better put, can you move adjacently to another number and cross the squares' boundaries?

Pretty fun puzzle!

Chris

A relative position in an adjacent square, to answer your first question. And to answer your second question, yes, you may cross the boundaries between squares.

So you could move from Bottom Left Number (BL#) in the Top Left Square (TL[]) to BL# in BL[]? Only if the number is different (so TR# TL[] > TR# BL[] wouldn't work?)

I'm not sure if I understand the movements here.

Yes. You can move there. Movements are allowed if the square you're currently on and the square you're going to have different numbers.

Great idea! This one wasn't too hard to solve but I think it has lots of potential.

You don’t need to go to all the numbers right?

No. Just from one corner to the opposite corner.

I found that if crossing boundaries are not allowed, the maze is on a tesseract:

where the vertices are labeled by 0 and 1. An edge connecting a 0 to a 1 is allowed and is in the green color.

If crossing boundaries are allowed, then I need to add some diagonal edges and break the symmetry of the tesseract.

Wow. Nice job, man. Crossing boundaries IS allowed, but I may have mazes with uncrossable boundaries, as well. What would the shape be on an 8x8 grid with 4x4 squares? or 2x2 squares?

I think a good name wold be a binary maze, as there are two values.

I'll think about it.

I thought of a good way to make an interactive version of this. I'll see if I can put something together for it.

Really? Let's see it!

I'm sure if Oskar had this idea he would put it on a 2x2. That would be kinda cool actually, but probably easy. Then again this is Oskar I am talking about.

Argh, haven't had time to code ANYTHING. D: Dog show all weekend. And I've never really worked with graphics or sprites. I should be able to do it, the logic is easy enough, I just want it to look nice, too.

Wow, I really like this idea.
Here's the solution I used (as a link so I don't spoil it for anyone)

Well, here's what an 8x8 grid for this puzzle might look like...

It seems kind of awkwardly divided up. But a 9x9 would look like this:

Just like a Sudoku grid!

I decided to try making a similar puzzle out of it. It uses four numbers instead of two. There are some special rules for this:
1. As before, you have to get from one corner to the other (start at orange and end at red)
2. Again as before, you can only move from a square to an adjacent square (no diagonals, "border crossing" is allowed), and from a square to a square in the same relative position in an adjacent 3x3 block.
3. However, when you do the first kind of move (square to adjacent square), the two numbers have to be next to each-other in the number line. For example, 2-3 is legal, 4-1 isn't, 1-3 isn't.
4. When you do the second kind of move (3x3 block to adjacent 3x3 block), the current number and the new number have to either both be even or both be odd. For example, 1-3 is legal, 4-2 is legal, 2-3 isn't.

As far as I know, there is only one major solution, good luck!


EDIT: It looks like there's more solutions than I thought...

@minstormscreator

Holy carp! Nice! I meant an 8x8 out of 2x2 squares.

How did you make this? Is it computer-generated? How did you make the grid? Is 1-1 on the big squares legal?

I didn't really want to use an odd-numbered big square size because if an even one is used, each big move changes the parity of your position. That could make for some interesting puzzles!

I'd do it, but I'm still in the process of learning Python. It'll be here, just you wait!

Whenever the puzzles get larger, the chances for multiple solutions also rises, so it is difficult to create a puzzle that only has one solution. What I do for those is try to find the optimal solution, but then again, how do I know there isn't one better? Still a great puzzle!

Chris

One of the first things I thought of was "You could add more numbers D: and make it be ordered D:".

Dog show again tomorrow, plus I just got my Curvy Copter. D: Java app or Flash version of this coming soonish.

Schuma, what would happen two-dimensionally if you inverted the tesseract?

Alright, so who's gonna be the first person to develop an algorithm for generating these mazes?